2024/05/26 更新

写真a

サワノ ヨシヒロ
澤野 嘉宏
SAWANO Yoshihiro
所属
理工学部 教授
その他担当機関
理工学研究科数学専攻博士課程前期課程
理工学研究科数学専攻博士課程後期課程
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プロフィール
中央大学の澤野嘉宏です。調和解析を中心とした解析学を研究しております。拙著ベゾフ空間論、(英訳Theory of Besov spaces)、Theory of reproducing kernel Hilbert spaces, Morrey spacesなどを書いてわたくしの研究内容を説明しております。
外部リンク

学位

  • 博士(数理科学) ( 東京大学 )

  • 修士(数理科学) ( 東京大学 )

学歴

  • 2006年3月
     

    東京大学   数理科学研究科   数理科学専攻   博士後期   修了

  • 2004年3月
     

    東京大学   数理科学研究科   数理科学専攻   博士前期   修了

  • 2002年3月
     

    東京大学   理学部   数学科   卒業

経歴

  • 2020年4月 - 現在

    中央大学   理工学部   教授

  • 2012年4月 - 2020年3月

    首都大学東京   理工学研究科   准教授

  • 2012年4月 - 2020年3月

    首都大学東京   理工学研究科   准教授

  • 2009年11月 - 2012年3月

    京都大学   理学部   助教

  • 2008年4月 - 2009年10月

    学習院大学   Faculty of Science

  • 2008年4月 - 2009年10月

    学習院大学

  • 2005年4月 - 2008年3月

    日本学術振興会特別研究員採用

  • 2005年 - 2007年

    日本学術振興会特別研究員採用

▼全件表示

所属学協会

  • 日本数学会

研究キーワード

  • ベゾフ空間

  • 再生核ヒルベルト空間

  • フーリエ解析

  • 測度論

  • モレー空間

  • 調和解析

  • 関数空間

  • 偏微分方程式

  • 実解析

研究分野

  • 自然科学一般 / 基礎解析学  / 解析学基礎

論文

  • Theory of Besov spaces 査読

    Yoshihiro Sawano

    Developments in Mathematics   56   1 - 938   2018年

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    担当区分:筆頭著者, 責任著者   掲載種別:論文集(書籍)内論文  

    DOI: 10.1007/978-981-13-0836-9_1

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  • Extrapolation to two-weighted Herz spaces with three variable exponents

    Mitsuo Izuki, Takahiro Noi, Yoshihiro Sawano

    Advances in Operator Theory   9 ( 3 )   2024年4月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media LLC  

    DOI: 10.1007/s43036-024-00333-w

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    その他リンク: https://link.springer.com/article/10.1007/s43036-024-00333-w/fulltext.html

  • Non-smooth atomic decomposition of Triebel–Lizorkin-type spaces

    Yoshihiro Sawano, Dachun Yang, Wen Yuan

    Banach Journal of Mathematical Analysis   2024年4月

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    掲載種別:研究論文(学術雑誌)  

    DOI: 10.1007/s43037-023-00321-x

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  • Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit

    Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    Journal of Function Spaces   2024年1月

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    掲載種別:研究論文(学術雑誌)  

    DOI: 10.1155/2024/3262798

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  • On the Weak Boundedness of Multilinear Littlewood–Paley Functions

    Mahdi Hormozi, Yoshihiro Sawano, Kôzô Yabuta

    Journal of Fourier Analysis and Applications   2023年8月

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    掲載種別:研究論文(学術雑誌)  

    DOI: 10.1007/s00041-023-10030-6

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  • Weighted local Hardy spaces with variable exponents

    Mitsuo Izuki, Toru Nogayama, Takahiro Noi, Yoshihiro Sawano

    MATHEMATISCHE NACHRICHTEN   2023年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-V C H VERLAG GMBH  

    This paper defines local weighted Hardy spaces with variable exponents. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the functions in the Lebesgue spaces with exponentially decaying exponent. As applications, we obtain the boundedness of singular integral operators, the Littlewood-Paley characterization, and wavelet decomposition.

    DOI: 10.1002/mana.202200248

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  • Bourgain–Morrey spaces and their applications to boundedness of operators 査読

    Naoya Hatano, Toru Nogayama, Yoshihiro Sawano, Denny Ivanal Hakim

    Journal of Functional Analysis   284 ( 1 )   109720 - 109720   2023年1月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier BV  

    DOI: 10.1016/j.jfa.2022.109720

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  • Local and global solvability for Keller–Segel system in Besov–Morrey spaces 査読

    Toru Nogayama, Yoshihiro Sawano

    Journal of Mathematical Analysis and Applications   516 ( 1 )   126508 - 126508   2022年12月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier BV  

    DOI: 10.1016/j.jmaa.2022.126508

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  • Sparse Non-Smooth Atomic Decomposition of Quasi-Banach Lattices 招待 査読

    Naoya Hatano, Ryota Kawasumi, Yoshihiro Sawano

    Journal of Fourier Analysis and Applications   2022年8月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1007/s00041-022-09956-0

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  • A remark on the paper"Vector-valued operators with singular kernel and Triebel-Lizorkin block spaces with variable exponents" by Kwok Pun Ho 査読

    Naoya Hatano, Toru Nogayama, Yoshihiro Sawano

    Kyoto Journal of Mathematics   62 ( 2 )   357 - 375   2022年6月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    Our goal of this paper is to show that Ho's vector-valued Morrey spaces can be realized as a special case of pointwise multiplier spaces. This extends Lemarié- Rieusset's theorem. One cannot extend his theorem directly, because we are handling Banach lattices instead of Lebesgue spaces. It turns out that mixed Morrey spaces, Lorentz-Morrey spaces, and Orlicz-Morrey spaces fall under the scope of the framework in this paper. This work can be located as a continuation of the huge study of multiplier spaces collected in the book of Maz'ya.

    DOI: 10.1215/21562261-2022-0008

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  • Spaceability on Morrey Spaces 査読

    Y. Sawano, S. M. Tabatabaie

    Iranian Journal of Mathematical Sciences and Informatics   17 ( 1 )   219 - 225   2022年4月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:CMV Verlag  

    DOI: 10.52547/ijmsi.17.1.219

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  • Multiplier conditions for Boundedness into Hardy spaces 査読

    Loukas Grafakos, Shohei Nakamura, Hanh Van Nguyen, Yoshihiro Sawano

    Annales de l'Institut Fourier   71 ( 3 )   1047 - 1064   2022年3月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Cellule MathDoc/CEDRAM  

    DOI: 10.5802/aif.3416

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  • Atomic and Wavelet Characterization of Musielak–Orlicz Hardy Spaces for Generalized Orlicz Functions 査読

    Mitsuo Izuki, Eiichi Nakai, Yoshihiro Sawano

    Integral Equations and Operator Theory   94 ( 1 )   2022年3月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media {LLC}  

    DOI: 10.1007/s00020-021-02672-2

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  • Universality of neural networks with a sigmoidal activation or discriminatory function on Banach lattices over the real line 査読

    Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    Journal of Mathematical Science   2022年

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    記述言語:英語  

    DOI: 10.1007/s10958-022-05889-7

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  • Sharp Bounds for Certain m-linear Integral Operators on p-adic Function Spaces 査読

    Tserendorj Batbold, Yoshihiro Sawano, Ganbaatar Tumendemberel

    Filomat   36 ( 3 )   801 - 812   2022年

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    掲載種別:研究論文(学術雑誌)  

    In this paper, we establish necessary and sufficient conditions for boundedness of m-linear p-adic integral operators with general homogeneous kernel on p-adic Lebesgue spaces and p-adic Morrey spaces, respectively. In each case, we obtain the corresponding operator norms. Also, we deal with some particular examples and compare them with the previously known from the literature.

    DOI: 10.2298/FIL2203801B

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  • A note on the paper “Singular integral operators in generalized Morrey spaces on curves in the complex plane”, Mediterr. J. Math. (2017) 14: 203. doi.org/10.1007/s00009-017-1004-9, by E. Burtseva 査読

    Vagif S. Guliyev, Yoshihiro Sawano

    Journal of Mathematical Inequalities   ( 1 )   345 - 346   2022年

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    担当区分:筆頭著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Element d.o.o.  

    DOI: 10.7153/jmi-2022-16-24

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  • Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents 査読

    Mitsuo Izuki, Toru Nogayama, Takahiro Noi, Yoshihiro Sawano

    Constructive Approximation   2022年

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)  

    The goal of this paper is to define local weighted variable Sobolev spaces of fractional and negative order and their characterization by wavelets. We first consider local weighted variable Sobolev spaces by means of weak derivatives and obtain a wavelet characterization for these spaces. Using the Bessel potentials, we next define local weighted variable Sobolev spaces of fractional order. We show that Sobolev spaces obtained by weak derivatives and those by the Bessel potentials coincide. Finally, using duality, we define local weighted variable Sobolev spaces with negative order. We also show that local weighted variable Sobolev spaces are closed under complex interpolation. Some examples are given including the applications to weighted uniformly local Lebesgue spaces with variable exponents and periodic function spaces as a by-product, although the exponent is constant.

    DOI: 10.1007/s00365-022-09573-6

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  • Relatively Compact Sets in Variable Exponent Morrey Spaces on Metric Spaces 査読

    Rovshan A. Bandaliyev, Przemysław Górka, Vagif S. Guliyev, Yoshihiro Sawano

    Mediterranean Journal of Mathematics   18 ( 6 )   2021年12月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media LLC  

    Abstract

    We study a characterization of the precompactness of sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally bounded sets are characterized from several points of view for the case of variable exponent Morrey spaces over metric measure spaces. This characterization is new in the case of constant exponents.

    DOI: 10.1007/s00009-021-01828-z

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    その他リンク: https://link.springer.com/article/10.1007/s00009-021-01828-z/fulltext.html

  • Fractional Maximal Operator on Musielak–Orlicz Spaces Over Unbounded Quasi-Metric Measure Spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Results in Mathematics   76 ( 4 )   2021年12月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media {LLC}  

    DOI: 10.1007/s00025-021-01490-7

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  • Complex interpolation of variable Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    Mathematische Nachrichten   294 ( 11 )   2140 - 2150   2021年11月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Wiley  

    DOI: 10.1002/mana.202000513

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    その他リンク: https://onlinelibrary.wiley.com/doi/full-xml/10.1002/mana.202000513

  • Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces 査読

    Eiichi Nakai, Yoshihiro Sawano

    Mathematics   2021年10月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    DOI: 10.3390/math9212754

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  • Atomic Decomposition for Mixed Morrey Spaces 査読

    Toru Nogayama, Takahiro Ono, Daniel Salim, Yoshihiro Sawano

    The Journal of Geometric Analysis   31 ( 9 )   9338 - 9365   2021年9月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media LLC  

    DOI: 10.1007/s12220-020-00513-z

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    その他リンク: https://link.springer.com/article/10.1007/s12220-020-00513-z/fulltext.html

  • Inclusions in Generalized Orlicz Spaces 査読

    Yoshihiro Sawano, Seyyed Mohammad Tabatabaie

    Bulletin of the Iranian Mathematical Society   47 ( 4 )   1227 - 1233   2021年8月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER SINGAPORE PTE LTD  

    In this paper, we give some equivalent conditions to have an inclusion between two generalized Orlicz spaces. One of these conditions does not depend on generalized Young functions. The obtained results improve the famous ones on Lebesgue spaces.

    DOI: 10.1007/s41980-020-00437-y

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  • Disjoint dynamics of weighted translations on solid spaces 査読

    Yoshihiro Sawano, Seyyed Mohammad Tabatabaie, Fatemeh Shahhoseini

    Topology and its Applications   298   2021年7月

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    担当区分:筆頭著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELSEVIER  

    In this paper, applying the new concept of aperiodic functions, we characterize disjoint hypercyclic and disjoint topologically mixing weighted translation operators on general Banach lattices. The obtained results in addition to previous modes of Lebesgue and Orlicz spaces, also cover new classes such as some closed subspaces of Morrey spaces.

    DOI: 10.1016/j.topol.2021.107709

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  • Complex interpolation of the predual of Morrey spaces over measure spaces 査読

    Victor I. Burenkov, Denny I. Hakim, Eiichi Nakai, Yoshihiro Sawano, Takuya Sobukawa, Tamara V. Tararykova

    Georgian Mathematical Journal   28 ( 3 )   341 - 348   2021年6月

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    掲載種別:研究論文(学術雑誌)  

    We prove that block spaces defined on ℝn with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product.

    DOI: 10.1515/gmj-2019-2070

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  • Weighted Hankel Transform and Its Applications to Fourier Transform 査読

    Masami Okada, Yoshihiro Sawano

    Journal of Fourier Analysis and Applications   27 ( 2 )   2021年4月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)  

    The purpose of the present paper is to discuss the integrability of the Fourier transform of L∞-functions subject to a very weak decay condition. This will include the negative power of the logarithm. For a start, the case when d= 1 is investigated by the use of the second mean value theorem. Based on the discussion of this case, a passage to the weighted Hankel transform is done, which covers the integrability of the d-dimensional Fourier transform of the radial functions.

    DOI: 10.1007/s00041-021-09831-4

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  • Generalized fractional integral operators on Orlicz–Hardy spaces 査読

    Ryutaro Arai, Eiichi Nakai, Yoshihiro Sawano

    Mathematische Nachrichten   294 ( 2 )   224 - 235   2021年2月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Wiley  

    The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space (Formula presented.) to another Orlicz–Hardy space (Formula presented.), where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator (Formula presented.) from (Formula presented.) to (Formula presented.) for (Formula presented.) and (Formula presented.), which was proved by Stein and Weiss in 1960.

    DOI: 10.1002/mana.201900052

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  • Complex Interpolation and the Adams Theorem 査読

    Yoshihiro Sawano, Satoko Sugano

    Potential Analysis   54 ( 2 )   299 - 305   2021年2月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media {LLC}  

    Recently, many researchers investigated the description of the complex interpolation of Morrey spaces. Among others, the second complex interpolation of Morrey spaces turned out to be the Calderón product of Morrey spaces. In this paper as an application of this fact, we propose an improvement of the Adams theorem asserting that the fractional integral operator maps Morrey spaces to other Morrey spaces.

    DOI: 10.1007/s11118-020-09827-7

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  • On the compactness and spectra of the generalized difference operator on the spaces ℓ and bv 査読

    Saad R. El-Shabrawy, Yoshihiro Sawano

    Operators and Matrices   15 ( 3 )   959 - 983   2021年

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    掲載種別:研究論文(学術雑誌)  

    In this paper, we consider the compactness and the spectrum of the generalized difference operator Δab on the Banach sequence spaces ℓ∞, of bounded sequences, and bv, of bounded variation sequences, which allows us to generalize and extend some existing results for the operator Δab . Furthermore, the results for the operator Δab on ℓ∞ are new even in the case where Δab is reduced to the difference operator Δ .

    DOI: 10.7153/oam-2021-15-62

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  • Singular integral operators acting on Orlicz-Morrey spaces of the first kind 招待 査読

    Yoshihiro Sawano

    Nonlinear Studies   2021年

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    担当区分:筆頭著者, 責任著者  

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  • A Refinement of the Adams Theorem on the Riesz Potential 招待 査読

    Yoshihiro Sawano

    Springer Proceedings in Mathematics and Statistics   357   497 - 506   2021年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(国際会議プロシーディングス)   出版者・発行元:Springer International Publishing  

    The goal of this note is to consider the application of the complex interpolation space of Morrey spaces. Actually, the boundedness of Riesz potentials acting on Morrey spaces, which is obtained by Adams, is refined by means of the complex interpolation.

    DOI: 10.1007/978-3-030-77493-6_29

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  • Local Muckenhoupt class for variable exponents 査読

    Toru Nogayama, Yoshihiro Sawano

    Journal of Inequalities and Applications   2021 ( 1 )   2021年

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    掲載種別:研究論文(学術雑誌)  

    This work extends the theory of Rychkov, who developed the theory of Aploc weights. It also extends the work by Cruz-Uribe SFO, Fiorenza, and Neugebauer. The class Ap(⋅)loc is defined. The weighted inequality for the local Hardy–Littlewood maximal operator on Lebesgue spaces with variable exponents is proven. Cruz-Uribe SFO, Fiorenza, and Neugebauer considered the Muckenhoupt class for Lebesgue spaces with variable exponents. However, due to the setting of variable exponents, a new method for extending weights is needed. The proposed extension method differs from that by Rychkov. A passage to the vector-valued inequality is realized by means of the extrapolation technique. This technique is an adaptation of the work by Cruz-Uribe and Wang. Additionally, a theory of extrapolation adapted to our class of weights is also obtained.

    DOI: 10.1186/s13660-021-02601-2

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  • The spectra of the generalized difference operators on the spaces of convergent series 査読

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Linear and Multilinear Algebra   69 ( 4 )   732 - 751   2021年

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Informa {UK} Limited  

    An investigation is made on the spectrum and fine spectrum of the generalized difference operator (Formula presented.) on the space (Formula presented.) of convergent series. Some related results, concerning the spectrum of the adjoint operator (Formula presented.) on the space (Formula presented.) of bounded variation sequences, are also derived. Further, some special cases of the main results are investigated deeper.

    DOI: 10.1080/03081087.2019.1617231

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  • Cantor functions associated with generalized expansions 査読

    Yoshihiro Sawano, Haruka Fujiwara

    Transactions Issue Mathematics, Azerbaijan National Academy of Sciences   41 ( 4 )   136 - 141   2021年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    The goal of this note is to propose an expansion of real numbers, which generalizes the binary and ternary expansions. As an application of this expansion, the ternary Cantor function is generalized to the one adapted to the expansion. This generalized Cantor function can be adjusted to have the set of discontinuity of any Hausdorff dimension.

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  • Boundedness of composition operators on Morrey spaces and weak Morrey spaces 査読

    Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    Journal of Inequalities and Applications   2021 ( 1 )   2021年

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    掲載種別:研究論文(学術雑誌)  

    In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As this specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.

    DOI: 10.1186/s13660-021-02599-7

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  • Applications of interpolation methods and Morrey spaces to elliptic PDEs 査読

    Mieczysław Mastyło, Yoshihiro Sawano

    ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE   999 - 1021   2020年12月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Scuola Normale Superiore - Edizioni della Normale  

    DOI: 10.2422/2036-2145.201807_001

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  • Some modular inequalities in lebesgue spaces with a variable exponent 査読

    Mitsuo Izuki, Takahiro Noi, Yoshihiro Sawano

    Transactions of A. Razmadze Mathematical Institute   174 ( 3 )   343 - 349   2020年12月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)  

    Our aim is to study the modular inequalities for some operators, for example, the Bergman projection in Lebesgue spaces with a variable exponent. Under proper assumptions on the variable exponent, we prove that the modular inequalities hold, if and only if the exponent almost everywhere is equal to a constant. In order to get the main results, we establish a lower pointwise bound for these operators of a characteristic function.

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  • Sparse non-smooth atomic decomposition of Morrey spaces 査読

    Yoshihiro Sawano

    Mathematical Methods in the Applied Sciences   43 ( 16 )   9320 - 9326   2020年11月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(国際会議プロシーディングス)   出版者・発行元:Wiley  

    Recently, a non-smooth atomic decomposition in Morrey spaces was obtained by the author, Iida and Tanaka. This note refines the above existing result using the notion of sparse families. As an application, we prove the equivalence between fractional integral operators and fractional maximal operators under the Morrey norm.

    DOI: 10.1002/mma.6112

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    その他リンク: https://onlinelibrary.wiley.com/doi/full-xml/10.1002/mma.6112

  • Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Georgian Mathematical Journal   27 ( 3 )   433 - 439   2020年9月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WALTER DE GRUYTER GMBH  

    The predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

    DOI: 10.1515/gmj-2018-0068

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  • Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent 査読

    Mitsuo Izuki, Toru Nogayama, Takahiro Noi, Yoshihiro Sawano

    Nonlinear Analysis, Theory, Methods and Applications   198   111930 - 111930   2020年9月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier {BV}  

    Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular inequalities to hold. One big achievement is that the weights with exponential growth can be handled in the framework of variable exponents.

    DOI: 10.1016/j.na.2020.111930

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    その他リンク: http://arxiv.org/pdf/1912.03400v1

  • Bilinear rough singular integral operators on Morrey spaces 査読

    Daniel Salim, Yoshihiro Sawano, Pebrudal Zanu

    Journal of Analysis   28 ( 3 )   817 - 825   2020年9月

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    担当区分:責任著者   掲載種別:研究論文(学術雑誌)  

    Recently Grafakos et al., have proved that the bilinear rough singular integral operators are bounded on Lebesgue spaces. Here we aim to show that these operators extend to bounded linear operators on Morrey spaces as well. Although the proof hinges on the boundedness due to Grafakos et al., the proof seems to give a general technique to prove or extend the boundedness of the operators.

    DOI: 10.1007/s41478-019-00206-z

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  • Complex interpolation of various subspaces of Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    Science China Mathematics   63 ( 5 )   937 - 964   2020年5月

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces. We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al. (2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano (2017) and Hakim et al. (2017).

    DOI: 10.1007/s11425-017-9318-0

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  • Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces 査読

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Monatshefte fur Mathematik   192 ( 1 )   185 - 224   2020年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER WIEN  

    This paper concerns the spectrum and the fine spectrum of the discrete generalized Cesàro operator Ct, where 0 ≤ t< 1 , on Banach sequence spaces close to ℓ1 and ℓ∞. We derive some compactness results for the operator Ct to describe the spectrum. Our technique involves standard operator theory and summability theory.

    DOI: 10.1007/s00605-020-01376-w

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  • Homogeneous Besov spaces 招待 査読

    Yoshihiro Sawano

    Kyoto Journal of Mathematics   60 ( 1 )   1 - 43   2020年4月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:DUKE UNIV PRESS  

    This note is based on a series of lectures delivered at Kyoto University in 2015. This note surveys the homogeneous Besov space Bspq on ℝn with 1 < p, q < ∞ and s ∈ ℝ in a rather self-contained manner. Among other results, we show that S′∞ and S′/P are isomorphic, and we also discuss the realizations in Bspq. The fact that S′∞ and S′/P are isomorphic can be found in textbooks. The realization of Bspq can be found in works by Bahouri, Chemin, and Danchin and by Bourdaud for example. Here, we prove these facts using fundamental results in functional analysis such as the Hahn-Banach extension theorem.

    DOI: 10.1215/21562261-2019-0038

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  • Generalized Riesz potentials of functions in Morrey spaces L (1,φ;κ)(G) over non-doubling measure spaces 査読

    Yoshihiro Sawano, Masaki Shigematsu, Tetsu Shimomura

    Forum Mathematicum   32 ( 2 )   339 - 359   2020年3月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WALTER DE GRUYTER GMBH  

    This paper proves the boundedness of the generalized Riesz potentials I ρ, μ, τ ⁢ f {I_{\rho,\mu,\tau}f} of functions in the Morrey space L (1, φ; κ) ⁢ (G) {L^{(1,\varphi;\kappa)}(G)} over a general measure space X, with G a bounded open set in X (or G is X) {X)}, as an extension of earlier results. The modification parameter τ is introduced for the purpose of including the case where the underlying measure does not satisfy the doubling condition. What is new in the present paper is that ρ depends on x ∈ X {x\in X}. An example in the end of this article convincingly explains why the modification parameter τ must be introduced.

    DOI: 10.1515/forum-2019-0140

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  • A Weak Type Vector-Valued Inequality for the Modified Hardy-Littlewood Maximal Operator for General Radon Measure on Rn 査読

    Yoshihiro Sawano

    Analysis and Geometry in Metric Spaces   8 ( 1 )   261 - 267   2020年1月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:DE GRUYTER POLAND SP Z O O  

    The aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy-Littlewood maximal operator for general Radon measure on Rn. Earlier, the strong type vector-valued inequality for the same operator and the weak type vector-valued inequality for the dyadic maximal operator were obtained. This paper will supplement these existing results by proving a weak type counterpart.

    DOI: 10.1515/agms-2020-0113

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    その他リンク: https://www.degruyter.com/document/doi/10.1515/agms-2020-0113/xml

  • Dissertationes mathematicae 査読

    Yuzuru Inahama, Yoshihiro Sawano

    Dissertationes Mathematicae   558   2020年

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    掲載種別:研究論文(学術雑誌)  

    We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus. This equation is highly singular and basically ill-posed in its original form. The main objective of the present paper is to formulate and solve this equation locally in time in the framework of paracontrolled calculus when the differential order of the main term, the fractional Laplacian, is larger than 7=4. No renormalization has to be done for this model.

    DOI: 10.4064/dm806-7-2020

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  • Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over quasi-metric measure spaces 査読

    Daiki Hashimoto, Yoshihiro Sawano, Tetsu Shimomura

    Colloquium Mathematicum   161 ( 1 )   51 - 66   2020年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    Our aim in this paper is to give a Gagliardo-Nirenberg inequality for generalized Riesz potentials Iρ,µ,κf of functions in Musielak-Orlicz spaces over quasimetric measure spaces, as an extension of work of Mizuta et al. (2012). What is new in this paper is that ρ depends on (Formula Presented) and that the underlying measure µ is not doubling.

    DOI: 10.4064/cm7535-4-2019

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  • Weighted local morrey spaces 査読

    Shohei Nakamura, Yoshihiro Sawano, Hitoshi Tanaka

    Annales Academiae Scientiarum Fennicae Mathematica   45 ( 1 )   67 - 93   2020年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    We discuss the boundedness of linear and sublinear operators in two types of weighted local Morrey spaces. One is defined by Natasha Samko in 2008. The other is defined by Yasuo Komori-Furuya and Satoru Shirai in 2009. We characterize the class of weights for which the Hardy-Littlewood maximal operator is bounded. Under a certain integral condition it turns out that the singular integral operators are bounded if and only if the Hardy-Littlewood maximal operator is bounded. As an application of the characterization, the power weight function [pipe] · [pipe] is considered. The condition on α for which the Hardy-Littlewood maximal operator is bounded can be described completely.

    DOI: 10.5186/aasfm.2020.4504

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  • Correction to: Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces (Monatshefte für Mathematik, (2020), 10.1007/s00605-020-01376-w) 査読

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Monatshefte fur Mathematik   2020年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER WIEN  

    In the original article, in Theorem 7.4 (in all statements from (1) to (9)): the symbol C0 should be replaced by bv.

    DOI: 10.1007/s00605-020-01401-y

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  • Uniform boundedness of szász–mirakjan–kantorovich operators in morrey spaces with variable exponents 査読

    Yoshihiro Sawano, Xinxin Tian, Jingshi Xu

    Filomat   34 ( 7 )   2109 - 2121   2020年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:UNIV NIS, FAC SCI MATH  

    The Szász–Mirakjan–Kantorovich operators and the Baskakov–Kantorovich operators are shown to be controlled by the Hardy–Littlewood maximal operator. The Szász–Mirakjan–Kantorovich operators and the Baskakov–Kantorovich operators turn out to be uniformly bounded in Lebesgue spaces and Morrey spaces with variable exponents when the integral exponent is global log-Hölder continuous.

    DOI: 10.2298/FIL2007109S

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  • A global universality of two-layer neural networks with ReLU activations. 査読

    Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    CoRR   abs/2011.10225   1 - 3   2020年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Hindawi Limited  

    In the present study, we investigate a universality of neural networks, which concerns a density of the set of two-layer neural networks in function spaces. There are many works that handle the convergence over compact sets. In the present paper, we consider a global convergence by introducing a norm suitably, so that our results will be uniform over any compact set.

    DOI: 10.1155/2021/6637220

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    その他リンク: https://dblp.uni-trier.de/db/journals/corr/corr2011.html#abs-2011-10225

  • On the equivalence of the K-functional and the modulus of continuity on the Morrey spaces 査読

    Victor Burenkov, Arash Ghorbanalizadeh, Yoshihiro Sawano

    Journal of Approximation Theory   248   2019年12月

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    掲載種別:研究論文(学術雑誌)  

    In this note, the Morrey spaces and the Sobolev–Morrey spaces are considered. In particular, the K-functional with respect to these spaces is estimated from above and below. As an application, we characterize the Nikol'skii–Besov–Morrey spaces via real interpolation.

    DOI: 10.1016/j.jat.2019.105295

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  • On the Strichartz estimates for orthonormal systems of initial data with regularity 査読

    Neal Bez, Younghun Hong, Sanghyuk Lee, Shohei Nakamura, Yoshihiro Sawano

    Advances in Mathematics   354   2019年10月

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    掲載種別:研究論文(学術雑誌)  

    The classical Strichartz estimates for the free Schrödinger propagator have recently been substantially generalised to estimates of the form ‖∑jλj|eitΔfj|2‖LptLxq≲‖λ‖ℓα for orthonormal systems (fj)j of initial data in L2, firstly in work of Frank–Lewin–Lieb–Seiringer and later by Frank–Sabin. The primary objective is identifying the largest possible α as a function of p and q, and in contrast to the classical case, for such estimates the critical case turns out to be [Formula presented]. We consider the case of orthonormal systems (fj)j in the homogeneous Sobolev spaces H˙s for [Formula presented] and we establish the sharp value of α as a function of p, q and s, except possibly an endpoint in certain cases. Furthermore, at the critical case [Formula presented] for general s, we show the veracity of the desired estimates when α=p if we consider frequency localised estimates, and the failure of the (non-localised) estimates when α=p; this exhibits the difficulty of upgrading from frequency localised estimates in this context, again in contrast to the classical setting.

    DOI: 10.1016/j.aim.2019.106736

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  • Riesz transform and fractional integral operators generated by nondegenerate elliptic differential operators 査読

    Yoshihiro Sawano, Denny Ivanal Hakim, Daniel Salim

    Advances in Operator Theory   4 ( 4 )   750 - 766   2019年9月

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    掲載種別:研究論文(学術雑誌)  

    The Morrey boundedness is proved for the Riesz transform and the inverse operator of the nondegenerate elliptic differential operator of divergence form generated by a vector-function in (L ∞ )n 2 , and for the inverse operator of the Schrödinger operators whose nonnegative potentials satisfy a certain integrability condition. In this note, our result is not obtained directly from the estimates of integral formula, which reflects the fact that the solution of the Kato conjecture did not use any integral expression of the operators. One of the important tools in the proof is the decomposition of the functions in Morrey spaces based on the elliptic differential operators in question. In some special cases where the integral kernel comes into play, the boundedness property of the Littlewood-Paley operator was already obtained by Gong. So, the main novelties of this paper are the decomposition results associated with elliptic differential operators and the result in the case where the explicit formula of the integral kernel of the heat semigroup is unavailable.

    DOI: 10.15352/aot.1812-1443

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  • Approximation by trigonometric polynomials in variable exponent Morrey spaces 査読

    Vagif S. Guliyev, Arash Ghorbanalizadeh, Yoshihiro Sawano

    Analysis and Mathematical Physics   9 ( 3 )   1265 - 1285   2019年9月

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    掲載種別:研究論文(学術雑誌)  

    We investigate the direct and inverse theorems for trigonometric polynomials in the Morrey space Mp(·),λ(·) with variable exponents. For this space, we obtain estimates of the K-functional in terms of the modulus of smoothness and the Bernstein type inequality for trigonometric polynomials.

    DOI: 10.1007/s13324-018-0231-y

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  • Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind 査読

    Fatih Deringoz, Vagif S. Guliyev, Eiichi Nakai, Yoshihiro Sawano, Minglei Shi

    Positivity   23 ( 3 )   727 - 757   2019年7月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media {LLC}  

    In the present paper, we will characterize the boundedness of the generalized fractional integral operators Iρ and the generalized fractional maximal operators Mρ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators Mρ and Iρ on generalized Orlicz–Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators Mρ and Iρ on generalized Orlicz–Morrey spaces.

    DOI: 10.1007/s11117-018-0635-9

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  • Some Modular Inequalities in Lebesgue Spaces with Variable Exponent on the Complex Plane 査読

    M. Izuki, T. Koyama, T. Noi, Y. Sawano

    Mathematical Notes   106 ( 1-2 )   229 - 234   2019年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We consider the modular inequalities for some linear operators on Lebesgue spaces with variable exponent on the complex plane. The main results show that the variable exponent must be constant if modular inequalities hold.

    DOI: 10.1134/S0001434619070265

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  • Orlicz-fractional maximal operators on weighted Lp spaces 査読

    Takeshi Iida, Yoshihiro Sawano

    Journal of Mathematical Inequalities   13 ( 2 )   369 - 413   2019年6月

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    掲載種別:研究論文(学術雑誌)  

    Necessary and sufficient conditions for weight norm inequalities on Lebesgue spaces to hold are given in the scale of Orlicz spaces for the fractional Orlicz maximal operators which generalizes the fractional maximal operators. A similar argument for the Orlicz maximal operators is due to Pérez, who generalizes for the Fefferman-Stein inequality. The main result is the Fefferman-Stein inequality for the fractional maximal operators of the Sawyer type and the Hardy-Littlewood-Sobolev type. In this paper, we establish that the Lp -boundedness and the Fefferman-Stein type inequality of Orlicz maximal operator are essentially equivalent to the Saywer type inequality for the fractional Orlicz maximal operators. These inequalities are stronger than the Hardy-Littlewood-Sobolev type inequalities. More generally, we consider several mixed strong type inequalities for the ordinary and generalized fractional Orlicz maximal operators. As an application, we investigate the weight norm inequalities of the commutator [b, Iα], where b ∈ BMO(ℝn), and Iα the fractional integral operator.

    DOI: 10.7153/jmi-2019-13-26

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  • COMPLEX INTERPOLATION OF SMOOTHNESS TRIEBEL-LIZORKIN-MORREY SPACES 招待 査読

    Math. J. Okayama Univ.   61   99 - 128   2019年2月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Non-smooth decomposition of homogeneous Triebel−Lizorkin−Morrey spaces

    Yoshihiro Sawano, Keisuke Asami

    Commentationes Mathematicae   58 ( 1-2 )   2019年1月

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    掲載種別:研究論文(学術雑誌)   出版者・発行元:Polish Mathematical Society  

    DOI: 10.14708/cm.v58i1-2.6381

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  • Boundedness of generalized Riesz potentials of functions in Morrey spaces L (1,ϕ</sup> ;κ ) (G) over non–doubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Mathematical Inequalities and Applications   22 ( 2 )   577 - 599   2019年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    Our aim in this paper is to deal with the boundedness of generalized Riesz potentials I ρ ,μ ,τ f of functions in Morrey spaces L (1, ϕ;κ ) (G) over non-doubling measure spaces, as an extension of [4, 6, 9, 12, 19]. The local integrability is assumed to be minimal, so that the results can not be obtained by the Hardy-Littlewood maximal operator. What is new in this paper is that ϕ depends on x ∈ X and that the underlying measure μ is not doubling.

    DOI: 10.7153/mia-2019-22-41

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  • Three geometric constants for morrey spaces 査読

    Hendra Gunawan, Eder Kikianty, Yoshihiro Sawano, Christopher Schwanke

    Bulletin of the Korean Mathematical Society   56 ( 6 )   1569 - 1575   2019年

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    掲載種別:研究論文(学術雑誌)  

    In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for L1 and L∞ spaces.

    DOI: 10.4134/BKMS.b190010

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  • Maximal operator on orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Proceedings of the American Mathematical Society   147 ( 7 )   2877 - 2885   2019年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)  

    In this paper, we are concerned with the boundedness of the Hardy-Littlewood maximal operator on the Orlicz space Lp(·) (log L)q(·)(X) of two variable exponents over unbounded quasi-metric measure spaces, as an extension of [Math Scand. 116 (2015), pp. 5–22]. The result is new even for the variable exponent Lebesgue space Lp(·) (X) in that the underlying spaces need not be bounded and that the underlying measure need not be doubling.

    DOI: 10.1090/proc/14225

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  • The John–Nirenberg inequality in ball Banach function spaces and application to characterization of BMO 査読

    出耒光夫, 野井貴弘, 澤野嘉宏

    Journal of Inequalities and Applications   2019 ( 1 )   2019年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1186/s13660-019-2220-6

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  • Complex interpolation and Calderón-Mityagin couples of morrey spaces 査読

    Mieczysław Mastyło, Yoshihiro Sawano

    Analysis and PDE   12 ( 7 )   1465 - 1494   2019年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(学術雑誌)   出版者・発行元:Mathematical Sciences Publishers  

    We study interpolation spaces between global Morrey spaces and between local Morrey spaces. We prove that for a wide class of couples of these spaces the upper complex Calderón spaces are not described by the K-method of interpolation. A by-product of our results is that couples of Morrey spaces belonging to this class are not Calderón-Mityagin couples. A Banach couple (X0,X1) is said to have the universal K-property if all relative interpolation spaces from any Banach couple to (X0,X1) are relatively K-monotone. A couple of local Morrey spaces is proved to have the universal K-property once it is a Calderón-Mityagin couple.

    DOI: 10.2140/apde.2019.12.1465

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  • A thought on generalized Morrey spaces 招待 査読

    Yoshihiro Sawano

    JOURNAL OF THE INDONESIAN MATHEMATICAL SOCIETY   25 ( 3 )   210 - 281   2018年12月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:INDONESIAN MATHEMATICAL SOC  

    Morrey spaces can complement the boundedness properties of operators that
    Lebesgue spaces can not handle. Morrey spaces which we have been handling are
    called classical Morrey spaces. However, classical Morrey spaces are not
    totally enough to describe the boundedness properties. To this end, we need to
    generalize parameters $p$ and $q$, among others $p$.

    DOI: 10.22342/jims.1.1.819.41-112

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    その他リンク: http://arxiv.org/pdf/1812.08394v1

  • Uniform boundedness of Kantorovich operators in Morrey spaces 招待 査読

    Yoshihiro Sawano

    22 ( 4 )   1097 - 1107   2018年9月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1007/s11117-018-0561-x

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  • A predual of a predual of Bσ and its applications to commutators 査読

    Yoshihiro Sawano, Hiroko Yoshida

    Science China Mathematics   61 ( 8 )   1437 - 1472   2018年8月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. A predual of Bσ-spaces is investigated. A predual of a predual of Bσ-spaces is also investigated, which can be used to investigate the boundedness property of the commutators. The relation between Herz spaces and local Morrey spaces is discussed. As an application of the duality results, one obtains the boundedness of the singular integral operators, the Hardy-Littlewood maximal operators and the fractional integral operators, as well as the commutators generated by the bounded mean oscillation (BMO) and the singular integral operators. What is new in this paper is that we do not have to depend on the specific structure of the operators. The results on the boundedness of operators are formulated in terms of Ḃσ-spaces and Bσ-spaces together with the detailed comparison of the ones in Herz spaces and local Morrey spaces. Another application is the nonsmooth atomic decomposition adapted to Bσ-spaces.

    DOI: 10.1007/s11425-017-9187-3

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  • Morrey-type Space and Its Köthe Dual Space 査読

    Mieczysław Mastyło, Yoshihiro Sawano, Hitoshi Tanaka

    Bulletin of the Malaysian Mathematical Sciences Society   41 ( 3 )   1181 - 1198   2018年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2016, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. We define Morrey-type spaces generated by a basis of measurable functions. The main result in this paper gives the description of the Köthe dual of these spaces. As an application, we recover many known cases including Mock Morrey spaces defined by David R. Adams.

    DOI: 10.1007/s40840-016-0382-7

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  • The Hardy and Heisenberg inequalities in Morrey spaces 査読

    Hendra Gunawan, Denny Ivanal Hakim, Eiichi Nakai, Yoshihiro Sawano

    Bulletin of the Australian Mathematical Society   97 ( 3 )   480 - 491   2018年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Cambridge University Press  

    We use the Morrey norm estimate for the imaginary power of the Laplacian to prove an interpolation inequality for the fractional power of the Laplacian on Morrey spaces. We then prove a Hardy-type inequality and use it together with the interpolation inequality to obtain a Heisenberg-type inequality in Morrey spaces.

    DOI: 10.1017/S0004972717001216

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    その他リンク: http://arxiv.org/pdf/1802.06531v1

  • Density, Duality and Preduality in Grand Variable Exponent Lebesgue and Morrey Spaces 査読

    Alexander Meskhi, Yoshihiro Sawano

    Mediterranean Journal of Mathematics   15 ( 3 )   2018年6月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Science and Business Media {LLC}  

    In this note some structural properties of grand variable exponent Lebesgue/Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of L∞ and the closure of Lp(·),λ(·) in grand variable exponent Morrey space Lp(·),λ(·),θ coincide if the measure of the underlying space is finite. Moreover, we get two different characterizations of this class. Further, duality and preduality of grand variable exponent Lebesgue spaces defined on quasi-metric measure spaces with σ-finite measure are obtained, which is new even when μ is finite.

    DOI: 10.1007/s00009-018-1145-5

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    その他リンク: http://arxiv.org/pdf/1710.02383v1

  • Generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Georgian Mathematical Journal   25 ( 2 )   303 - 311   2018年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Walter de Gruyter GmbH  

    In this paper, we aim to deal with the boundedness and the weak-Type boundedness for the generalized fractional integral operators on generalized Orlicz-Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 2017, 2, 159-190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 2017, 7, 534-546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

    DOI: 10.1515/gmj-2018-0018

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  • The Fractional Operators on Weighted Morrey Spaces 査読

    Shohei Nakamura, Yoshihiro Sawano, Hitoshi Tanaka

    Journal of Geometric Analysis   28 ( 2 )   1502 - 1524   2018年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer New York LLC  

    A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. The difference between the behavior of the fractional maximal operator and one of the fractional integral operator which originates from the structure of Morrey spaces will be clarified. The necessary and sufficient conditions are also verified for the power weights.

    DOI: 10.1007/s12220-017-9876-2

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    その他リンク: http://arxiv.org/pdf/1612.00663v1

  • Complex interpolation of Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    63 ( 4 )   569 - 590   2018年4月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1080/17476933.2017.1327954

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  • On inclusion relation between weak Morrey spaces and Morrey spaces 査読

    Hendra Gunawan, Denny Ivanal Hakim, Eiichi Nakai, Yoshihiro Sawano

    Nonlinear Analysis, Theory, Methods and Applications   168   27 - 31   2018年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Elsevier Ltd  

    In this paper, the size of the embedding constant from weak Morrey spaces into Morrey spaces is specified. As a by-product, the difference between weak Morrey spaces and Morrey spaces is clarified.

    DOI: 10.1016/j.na.2017.11.005

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  • New function spaces related to Morrey spaces and the Fourier transform 査読

    Shohei Nakamura, Yoshihiro Sawano

    Banach Journal of Mathematical Analysis   12 ( 1 )   1 - 30   2018年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Duke University Press  

    We introduce new function spaces to handle the Fourier transform on Morrey spaces and investigate fundamental properties of the spaces. As an application, we generalize the Stein-Tomas Strichartz estimate to our spaces. The geometric property of Morrey spaces and related function spaces will improve some well-known estimates.

    DOI: 10.1215/17358787-2017-0014

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  • Weak Morrey spaces with applications 査読

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Mathematische Nachrichten   291 ( 1 )   178 - 186   2018年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Wiley-VCH Verlag  

    The main object of this investigation is to study weak Morrey spaces. Block spaces, which are preduals of weak Morrey spaces, are characterized. Besides, the Fatou property of block spaces is proved. Finally, as an application, we study the boundedness of singular integral operators in weak Morrey spaces.

    DOI: 10.1002/mana.201700001

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  • On the boundedness of certain elliptic differential operators in generalized Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    2018年

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    担当区分:筆頭著者, 責任著者  

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  • Integral representation of the global minimizer. 査読

    Sho Sonoda, Isao Ishikawa, Masahiro Ikeda, Kei Hagihara, Yoshihiro Sawano, Takuo Matsubara, Noboru Murata

    CoRR   abs/1805.07517   2018年

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    掲載種別:研究論文(学術雑誌)  

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    その他リンク: https://dblp.uni-trier.de/db/journals/corr/corr1805.html#abs-1805-07517

  • Morrey spaces from various points of view 招待 査読

    Yoshihiro Sawano

    262   139 - 160   2018年

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    担当区分:筆頭著者, 責任著者   掲載種別:研究論文(国際会議プロシーディングス)  

    DOI: 10.1007/978-3-030-00874-1_5

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  • A remark on modified morrey spaces on metric measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura, Hitoshi Tanaka

    Hokkaido Mathematical Journal   47 ( 1 )   1 - 15   2018年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Morrey norms, which are originally endowed with two parameters, are considered on general metric measure spaces. Volberg, Nazarov and Treil showed that the modified Hardy-Littlewood maximal operator is bounded on Legesgue spaces. The modified Hardy-Littlewood maximal operator is known to be bounded on Morrey spaces on Euclidean spaces, if we introduce the third parameter instead of adopting a natural extension of Morrey spaces. When it comes to geometrically doubling, as long as an auxiliary parameter is introduced suitably, the Morrey norm does not depend on the third parameter and this norm extends naturally the original Morrey norm. If the underlying space has a rich geometric structure, there is still no need to introduce auxiliary parameters. However, an example shows that this is not the case in general metric measure spaces. In this paper, we present an example showing that Morrey spaces depend on the auxiliary parameters.

    DOI: 10.14492/hokmj/1520928055

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  • Applications: PDEs, the T1 theorem and related function spaces

    Yoshihiro Sawano

    Developments in Mathematics   56   565 - 707   2018年

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    掲載種別:論文集(書籍)内論文  

    As an application of what we have been gathering, we investigate partial differential equations. In Sect. 5.1, we develop a theory of function spaces on domains so as to consider partial differential equations on domains. To consider some solution operators we take up the pseudo-differential operators in Sect. 5.2. We apply what we have obtained to various equations such as heat equations, Schrödinger equations and wave equations in Sect. 5.3.

    DOI: 10.1007/978-981-13-0836-9_5

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  • Various function spaces

    Yoshihiro Sawano

    Developments in Mathematics   56   709 - 889   2018年

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    掲載種別:論文集(書籍)内論文  

    In recent decades, the subject of function spaces has undergone a rapid diversification and expansion, though the decomposition of functions and operators into simpler parts, mentioned in Chap. 4, remains a central tool and theme. One of the benefits in the theory of function spaces is that we can adjust many problems of function spaces in analysis when we handle some problems after familiarizing ourselves with the fundamental theory. In this book, we have been studying the huge development of the rich theory of function spaces.

    DOI: 10.1007/978-981-13-0836-9_6

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  • Relation with other function spaces

    Yoshihiro Sawano

    Developments in Mathematics   56   321 - 428   2018年

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    掲載種別:論文集(書籍)内論文  

    Although the definition of function spaces is complicated, we are still fascinated with Besov spaces and Triebel–Lizorkin spaces. One of the reasons, as we have alluded to in the preface, is that these scales realize many important function spaces.

    DOI: 10.1007/978-981-13-0836-9_3

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  • Decomposition of function spaces and its applications

    Yoshihiro Sawano

    Developments in Mathematics   56   429 - 564   2018年

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    掲載種別:論文集(書籍)内論文  

    The field of harmonic analysis dates back to the 19th century; the branch of function spaces dates back to the first half of 20th century, and has its roots in the study of the decomposition of functions using Fourier series and the Fourier transform. This aspect will be stressed for Besov spaces and Triebel–Lizorkin spaces. One of the elementary tools in harmonic analysis is to decompose functions or distributions into linear sums of elementary units.

    DOI: 10.1007/978-981-13-0836-9_4

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  • Elementary facts on harmonic analysis

    Yoshihiro Sawano

    Developments in Mathematics   56   1 - 204   2018年

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    掲載種別:論文集(書籍)内論文  

    Now we elaborate a fundamental theory of harmonic analysis. We aim here to collect fundamental facts on analysis and the tools which we use throughout this book.

    DOI: 10.1007/978-981-13-0836-9_1

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  • Besov spaces, Triebel–Lizorkin spaces and modulation spaces

    Yoshihiro Sawano

    Developments in Mathematics   56   205 - 320   2018年

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    掲載種別:論文集(書籍)内論文  

    Having set down elementary facts in the previous chapter, we take a detailed look at Besov spaces and Triebel–Lizorkin spaces, which are the main theme of this book. Chapter 2 is devoted to the introduction of elementary definitions together with some fundamental properties. First we define the Besov space Bspq(ℝn) with 1 ≤ p, q ≤∞ and s∈ ℝ in the spirit of Peetre, although Besov introduced Besov spaces in [171, 172]. After the Besov space Bspq(ℝn) for such a restricted case we define Aspq(ℝn), which unifies the Besov space Bspq(ℝn) with 0 < p, q ≤∞ and s∈ ℝ and the Triebel–Lizorkin space Fspq(ℝn) with 0 < p < ∞, 0 < q ≤∞ and s∈ ℝ.

    DOI: 10.1007/978-981-13-0836-9_2

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  • Weighted Morrey spaces--complex interpolation and the boundedness of the Hardy-Littlewood maximal operator 招待 査読

    Hakim, Denny Ivanal, Nakamura, Shohei, Sawano, Yoshihiro

    2018年

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    担当区分:筆頭著者, 責任著者  

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  • A Drosophila ex vivo model of olfactory appetitive learning 査読 国際誌

    Ema Suzuki-Sawano, Kohei Ueno, Shintaro Naganos, Yoshihiro Sawano, Junjiro Horiuchi, Minoru Saitoe

    Scientific Reports   7 ( 1 )   17725 - 17725   2017年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:NATURE PUBLISHING GROUP  

    During olfactory appetitive learning, animals associate an odor, or conditioned stimulus (CS), with an unconditioned stimulus (US), often a sugar reward. This association induces feeding behavior, a conditioned response (CR), upon subsequent exposure to the CS. In this study, we developed a model of this behavior in isolated Drosophila brains. Artificial activation of neurons expressing the Gr5a sugar-responsive gustatory receptor (Gr5a GRNs) induces feeding behavior in starved flies. Consistent with this, we find that in dissected brains, activation of Gr5a GRNs induces Ca2+ transients in motor neurons, MN11 + 12, required for ingestion. Significantly, activation of Gr5a GRNs can substitute for presentation of sugar rewards during olfactory appetitive learning. Similarly, in dissected brains, coincident stimulation of Gr5a GRNs and the antennal lobe (AL), which processes olfactory information, results in increased Ca2+ influx into MN11 + 12 cells upon subsequent AL stimulation. Importantly, olfactory appetitive associations are not formed in satiated flies. Likewise, AL-evoked Ca2+ transients in MN11 + 12 are not produced in ex vivo brains from satiated flies. Our results suggest that a starved/satiated state is maintained in dissected brains, and that this ex vivo system will be useful for identification of neural networks involved in olfactory appetitive learning.

    DOI: 10.1038/s41598-017-17955-1

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  • Complex Interpolation of Smoothness Morrey Subspaces 査読

    Denny Ivanal Hakim, Shohei Nakamura, Yoshihiro Sawano

    Constructive Approximation   46 ( 3 )   489 - 563   2017年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    Recently more and more attention has been paid to subspaces of Morrey spaces. The description of interpolation results for many of these spaces is found. However, the ones for smoothness Morrey subspaces are missing. The aim of this paper is to describe the output by the first and the second complex interpolations of these smoothness Morrey subspaces.

    DOI: 10.1007/s00365-017-9392-4

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  • A non-dense subspace in Mpq with 1<q<p<∞ 査読

    Yoshihiro Sawano

    Transactions of A. Razmadze Mathematical Institute   171 ( 3 )   379 - 380   2017年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2017 Ivane Javakhishvili Tbilisi State University The Morrey space Mq̃pis disproved dense in Mqpif 1&lt;q&lt;q̃&lt;p.

    DOI: 10.1016/j.trmi.2017.05.001

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  • Compactness of the commutators generated by Lipschitz functions and fractional integral operators 査読

    T. Nogayama, Y. Sawano

    Mathematical Notes   102 ( 5-6 )   687 - 697   2017年11月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:MAIK NAUKA/INTERPERIODICA/SPRINGER  

    Compactness of the commutator generated by fractional integral operators and Lipschitz functions is characterized, while its boundedness has already been characterized by Shirai.

    DOI: 10.1134/S0001434617110086

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  • Calderón’s First and Second Complex Interpolations of Closed Subspaces of Morrey Spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    Journal of Fourier Analysis and Applications   23 ( 5 )   1195 - 1226   2017年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2016, Springer Science+Business Media New York. In this paper, we are going to describe the first and second complex interpolations of closed subspaces of Morrey spaces, based on our previous results in [11]. Our results will be general enough because we are going to deal with abstract linear subspaces satisfying the lattice condition only. We also consider the closure in Morrey spaces on bounded domains of the set of smooth functions with compact support. Here, we do not require the smoothness condition on domains.

    DOI: 10.1007/s00041-016-9503-9

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  • Complex interpolation of grand Lebesgue spaces 査読

    Denny Ivanal Hakim, Mitsuo Izuki, Yoshihiro Sawano

    Monatshefte fur Mathematik   184 ( 2 )   245 - 272   2017年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER WIEN  

    The aim of this paper is to obtain the description of the first and second complex interpolations of grand Lebesgue spaces. We also investigate the complex interpolation of closed subspaces satisfying the lattice property.

    DOI: 10.1007/s00605-017-1022-5

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  • Decompositions of local Morrey-type spaces 査読

    Vagif S. Guliyev, Sabir G. Hasanov, Yoshihiro Sawano

    Positivity   21 ( 3 )   1223 - 1252   2017年9月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer Nature  

    We develop and apply a decomposition theory for generic local Morrey-type spaces. Our result is nonsmooth decomposition, which follows from the fact that local Morrey-type spaces are isomorphic to Hardy local Morrey-type spaces in the generic case. As an application of our results, we consider the Hardy operator.

    DOI: 10.1007/s11117-016-0463-8

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  • Elliptic equations with discontinuous coefficients in generalized Morrey spaces 査読

    Giuseppe Di Fazio, Denny Ivanal Hakim, Yoshihiro Sawano

    European Journal of Mathematics   3 ( 3 )   728 - 762   2017年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer International Publishing  

    We make a further step in the study of regularizing properties of the strong solutions to the equation [Equation not available: see fulltext.]where Ω is a bounded domain in Rn with smooth boundary. We are interested in estimating the second order derivatives of the solutions and in showing that solutions belong to the class C1,α. The relevant assumptions on the leading coefficients are uniform ellipticity and their membership to the class L∞∩ VMO. Moreover, the assumptions on the lower order term are optimal in the sense that they are assumed to belong to some generalized Morrey classes.

    DOI: 10.1007/s40879-017-0168-y

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  • Generalized fractional integral operators over non-doubling metric measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Integral Transforms and Special Functions   28 ( 7 )   534 - 546   2017年7月

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:TAYLOR & FRANCIS LTD  

    We shall deal with the boundedness and weak-type boundedness for the generalized fractional integral operators on generalized Orlicz-Morrey spaces LΦ, ϕ;2(x: μ) of the second kind over non-doubling metric measure spaces in this paper. We also discuss a necessary condition for the boundedness of the generalized fractional integral operators.

    DOI: 10.1080/10652469.2017.1318281

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  • Muckenhoupt–Wheeden conjectures for fractional integral operators 査読

    Yoshihiro Sawano, Satoko Sugano, Hitoshi Tanaka

    Journal of Mathematical Analysis and Applications   449 ( 1 )   456 - 463   2017年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2016 Elsevier Inc. The Muckenhoupt–Wheeden conjecture is disproved for fractional integral operator. Both the strong (p,p) and the weak (p,p) type conjectures are proved to be false. The arguments rely upon a property of the characteristic function of an approximating sequence of the Cantor set.

    DOI: 10.1016/j.jmaa.2016.11.074

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  • The singular integral operator and its commutator on weighted Morrey spaces 査読

    Shohei Nakamura, Yoshihiro Sawano

    Collectanea Mathematica   68 ( 2 )   145 - 174   2017年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER-VERLAG ITALIA SRL  

    In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the Aq-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.

    DOI: 10.1007/s13348-017-0193-7

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  • Sharp bounds for m-linear hilbert-type operators on the weighted morrey spaces 査読

    Tserendorj Batbold, Yoshihiro Sawano

    Mathematical Inequalities and Applications   20 ( 1 )   263 - 283   2017年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELEMENT  

    On the product of m weighted Morrey spaces, some m-linear operators are shown to be bounded. The operator norm is calculated explicitly. It may be interesting to compare the results for the Hardy operator and the ones for the Hardy-Littlewood maximal operator. In the end of this article, some concrete examples are presented.

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  • Pasting Reproducing Kernel Hilbert Spaces 査読

    Yoshihiro Sawano

    Trends in Mathematics   401 - 407   2017年

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    担当区分:筆頭著者, 責任著者   掲載種別:論文集(書籍)内論文   出版者・発行元:Springer International Publishing  

    DOI: 10.1007/978-3-319-48812-7_51

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  • An observation of the subspaces of S′ 招待 査読

    Yoshihiro Sawano

    Operator Theory: Advances and Applications   260   185 - 192   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:論文集(書籍)内論文  

    © 2017, Springer International Publishing AG. The spaces S′/P equipped with the quotient topology and S′∞ equipped with the weak-* topology are known to be homeomorphic, where P denotes the set of all polynomials. The proof is a combination of the fact in the textbook by Treves and the well-known bipolar theorem. In this paper by extending slightly the idea employed in [5], we give an alternative proof of this fact and then we extend this proposition so that we can include some related function spaces.

    DOI: 10.1007/978-3-319-51911-1_11

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  • Boundedness of the generalized fractional integral operators on generalized morrey spaces over metric measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Zeitschrift fur Analysis und ihre Anwendung   36 ( 2 )   159 - 190   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:EUROPEAN MATHEMATICAL SOC  

    Our aim in this paper is to deal with the boundedness of the generalized fractional integral operators on generalized Morrey spaces Lp;Ø;2(X; μ) over metric measure spaces. We also discuss a necessary condition for the boundedness of the generalized fractional integral operators. As applications, we establish new results for the predual spaces.

    DOI: 10.4171/ZAA/1584

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  • Generalized Hardy-Morrey spaces 査読

    A. Akbulut, V. S. Guliyev, T. Noi, Y. Sawano

    Zeitschrift fur Analysis und ihre Anwendung   36 ( 2 )   129 - 149   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:EUROPEAN MATHEMATICAL SOC  

    This paper is an off-spring of the contribution [Z. Anal. Anwend. 36 (2017)(1), 17-35]. We propose a way to consider the decomposition method of generalized Hardy-Morrey spaces. Generalized Hardy-Morrey spaces emerged from generalized Morrey spaces. By means of the grand maximal operator and the norm of generalized Morrey spaces, we can define generalized Hardy-Morrey spaces. With what we have culminated for the Hardy-Little wood maximal operator, we can easily refine the existing results. As an application, we consider bilinear estimates, which is the so-called Olsen inequality. In particular, our results complement the one in the 2014 paper by Iida, the fourth author and Tanaka [Z. Anal. Anwend. 33 (2014)(2), 149-170]; there were two mistakes. One lies in the decomposition result and another lies in the proof of the Olsen inequality.

    DOI: 10.4171/ZAA/1582

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  • Generalized morrey spaces-Revisited 査読

    Ali Akbulut, Vagif Sabir Guliyev, Takahiro Noi, Yoshihiro Sawano

    Zeitschrift fur Analysis und ihre Anwendung   36 ( 1 )   17 - 35   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:EUROPEAN MATHEMATICAL SOC  

    The generalized Morrey space Mp;φ(Rn) was defined by Mizuhara 1991 and Nakai in 1994. It is equipped with a parameter 0 < p < 1 and a function φ : Rn × (0) → (0). Our experience shows that Mp,φ(Rn) is easy to handle when 1 < p < 1. However, when 0 < p ≤ 1, the function space Mp,φ(Rn) is difficult to handle as many examples show. We propose a way to deal with Mp,φ(Rn) for 0 < p ≤ 1, in particular, to obtain some estimates of the Hardy-Littlewood maximal operator on these spaces. Especially, the vector-valued estimates obtained in the earlier papers are refined. The key tool is the weighted dual Hardy operator. Much is known on the weighted dual Hardy operator.

    DOI: 10.4171/ZAA/1577

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  • Characterization of BMO via ball Banach function spaces 査読

    出耒光夫, 澤野嘉宏

    Vestnik Sankt-Peterburgskogo Universiteta. Matematika. Mekhanika. Astronomiya   4(62)   78 - 86   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:日本語   掲載種別:研究論文(学術雑誌)  

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  • Sharpness of the brascamp-lieb inequality in lorentz spaces 査読

    Neal Bez, Sanghyuk Lee, Shohei Nakamura, Yoshihiro Sawano

    Electronic Research Announcements in Mathematical Sciences   24   53 - 63   2017年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:American Mathematical Society  

    We provide necessary conditions for the refined version of the Brascamp-Lieb inequality where the input functions are allowed to belong to Lorentz spaces, thereby establishing the sharpness of the range of Lorentz exponents in the subcritical case. Using similar considerations, some sharp refinements of the Strichartz estimates for the kinetic transport equation are established.

    DOI: 10.3934/era.2017.24.006

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  • Hardy spaces for ball quasi-Banach function spaces 査読

    Yoshihiro Sawano, Kwok Pun Ho, Dachun Yang, Sibei Yang

    Dissertationes Mathematicae   525 ( 525 )   1 - 102   2017年

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    担当区分:筆頭著者, 責任著者   記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN  

    This article unifies the theory for Hardy spaces built on Banach lattices on ℝn satisfying certain weak conditions on indicator functions of balls. The authors introduce a new family of function spaces, named the ball quasi-Banach function spaces, to define Hardy type spaces. The ones in this article extend classical Hardy spaces and include various known function spaces, for example, Hardy–Lorentz spaces, Hardy–Herz spaces, Hardy–Orlicz spaces, Hardy–Morrey spaces, Musielak–Orlicz–Hardy spaces, variable Hardy spaces and variable Hardy–Morrey spaces. Among them, Hardy–Herz spaces are shown to naturally arise in the context of any function spaces above. The example of Hardy–Morrey spaces shows that the absolute continuity of the quasi-norm is not necessary, which is used to guarantee the density of the set of functions having compact supports in Hardy spaces for ball quasi-Banach function spaces, but the decomposition result on these Hardy-type spaces never requires this absolute continuity of the quasi-norm. Moreover, via assuming that the powered Hardy–Littlewood maximal operator satisfies certain Fefferman–Stein vector-valued maximal inequality as well as it is bounded on the associate space, the atomic characterizations of Hardy type spaces are obtained. Although the results are based on the rather abstract theory of function spaces, they improve and extend the results for Orlicz spaces and Musielak–Orlicz spaces. Moreover, local Hardy type spaces and Hardy type spaces associated with operators in this setting are also studied.

    DOI: 10.4064/dm750-9-2016

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  • Generalized reproducing kernels and generalized delta functions 招待 査読

    2017年

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    担当区分:筆頭著者  

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  • A Multidimensional Integral Inequality Related to Hilbert-Type Inequality 査読

    Vandanjav Adiyasuren, Tserendorj Batbold, Yoshihiro Sawano

    Mediterranean Journal of Mathematics   13 ( 6 )   3837 - 3848   2016年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER BASEL AG  

    We present a multidimensional integral inequality related to the Hilbert-type inequality and the Carlson-type inequality. As an application, we obtain a sharper form of the Hilbert-type inequality. Carlson-type inequality is also considered.

    DOI: 10.1007/s00009-016-0717-5

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  • A note on the Kakeya maximal operator and radial weights on the plane

    Hiroki Saito, Yoshihiro Sawano

    Tohoku Mathematical Journal   68 ( 4 )   639 - 649   2016年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:TOHOKU UNIVERSITY  

    We obtain an estimate of the operator norm of the weighted Kakeya (Nikodým) maximal operator without dilation on L2(ω). Here we assume that aradial weight w satisfies the doubling and supremum condition. Recall that, in the definition of the Kakeya maximal operator, the rectangle in the supremum ranges over all rectangles in the plane pointed in all possible directions and having side lengths a and aN with N fixed. We are interested in its eccentricity N with a fixed. We give an example of a non-constant weight showing that √log N cannot be removed.

    DOI: 10.2748/tmj/1486177220

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  • Non-smooth Atomic Decompositions for Generalized Orlicz–Morrey Spaces of the Third Kind 査読

    Vagif S. Guliyev, Vagif S. Guliyev, Sabir G. Hasanov, Yoshihiro Sawano, Takahiro Noi

    Acta Applicandae Mathematicae   145 ( 1 )   133 - 174   2016年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2016, Springer Science+Business Media Dordrecht. We deal with the generalized Orlicz–Morrey space Mϕ,Φ(Rn) of the third kind and consider the decomposition method. Also we characterize its predual space. Some maximal estimates for generalized Orlicz–Morrey spaces of the third kind are also obtained by using the weighted Hardy operators. As an application, we consider the Olsen inequality, which is a bilinear estimate on the fractional integral operator. As an appendix, we consider a general form of the vector-valued boundedness of the Hardy–Littlewood maximal operator, where ϕ in the definition of Mϕ,Φ(Rn) depends on x as well. This paper contains a remedy for the mistake in the proof of the Olsen inequality of the 2014 paper by the second author (Iida et al. in Z. Anal. Anwend. 33(2):149–170, 2014).

    DOI: 10.1007/s10440-016-0052-7

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  • Boundedness of generalized fractional integral operators from the morrey space L<inf>1</inf>,φ(X; µ) to the campanato space L<inf>1</inf>,ψ(x; µ) over non-doubling measure spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano, Tetsu Shimomura

    Azerbaijan Journal of Mathematics   6 ( 2 )   117 - 127   2016年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2010 AZJM All rights reserved. The present paper supplements our earlier works. Our goal in the present paper is to establish the boundedness of generalized fractional integral operators from the Morrey space L1,φ(X; µ) to the Campanato space L1,ψ (X; µ) over non-doubling measure spaces (X, d, µ). What is new in the present paper is that µ satisfies a minimal condition; 0 = µ({x}) &lt; µ(B(x, r)) &lt; x for all x ∈ X and r &gt; 0. We first review some elementary facts on the fractional integral operators, generalized Morrey spaces, and analysis on metric measure spaces.

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  • Interpolation of generalized Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    Revista Matematica Complutense   29 ( 2 )   295 - 340   2016年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER-VERLAG ITALIA SRL  

    In this paper, we shall establish a theory of interpolation of generalized Morrey spaces. We use the complex interpolation methods. Our results extend the interpolation results for Morrey spaces which are discussed by Lu et al. (Can Math Bull 57:598–608, 2014), and also Lemarié-Rieusset (2014). We establish the interpolation of generalized weak Morrey spaces, generalized Orlicz–Morrey spaces and generalized weak Orlicz–Morrey spaces. We also consider the closure of the functions which are essentially bounded and have compact support. The second interpolation of such spaces will yield a class of closed spaces; we describe the second interpolation of the closure of the functions which are essentially bounded and have compact support. This result will carry over to generalized Morrey spaces, generalized weak Morrey spaces, generalized Orlicz–Morrey spaces and generalized weak Orlicz–Morrey spaces. We also give several examples that explain the subtlety of proving the interpolation of Morrey spaces.

    DOI: 10.1007/s13163-016-0192-3

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  • Generalized Morrey spaces and trace operator 査読

    Shohei Nakamura, Takahiro Noi, Yoshihiro Sawano

    Science China Mathematics   59 ( 2 )   281 - 336   2016年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SCIENCE PRESS  

    The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.

    DOI: 10.1007/s11425-015-5096-z

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  • Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz–Morrey spaces 査読

    Denny Ivanal Hakim, Eiichi Nakai, Yoshihiro Sawano

    Revista Matematica Complutense   29 ( 1 )   59 - 90   2016年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2015, Universidad Complutense de Madrid. In the present paper, we shall give a necessary and sufficient condition for the weak/strong boundedness of generalized fractional maximal operators on generalized Orlicz–Morrey spaces. We also give necessary and sufficient conditions for the vector-valued inequalities of the Hardy–Littlewood maximal operator, generalized fractional maximal operators and singular integral operators on these function spaces.

    DOI: 10.1007/s13163-015-0178-6

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  • Dissertationes Mathematicae 査読

    Ciqiang Zhuo, Yoshihiro Sawano, Dachun Yang

    Dissertationes Mathematicae   520   1 - 74   2016年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS  

    In this article, the authors introduce Hardy spaces with variable exponents, H*,p(·)(X), on RD-spaces with infinite measures via the grand maximal function. Then the authors characterize these spaces by means of the non-tangential maximal function or the dyadic maximal function. Characterizations in terms of atoms or Littlewood-Paley functions are also established. As applications, the authors prove an Olsen inequality for fractional integral operators and the boundedness of singular integral operators and quasi-Banach valued sublinear operators on these spaces. Finally, a duality theory of these spaces is developed.

    DOI: 10.4064/dm744-9-2015

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  • Some norm Inequalities In Musielak-Orlicz spaces 査読

    Fumi Yuki Maeda, Yoshihiro Sawano, Tetsu Shimomura

    Annales Academiae Scientiarum Fennicae Mathematica   41 ( 2 )   721 - 744   2016年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SUOMALAINEN TIEDEAKATEMIA  

    Our aim in this paper is to establish various norm inequalities in Musielak-Orlicz spaces. We give a generalization of a result due to Cruz-Uribe, Fiorenza, Martell and Pérez and apply it to obtain norm inequalities for classical operators as well as an Olsen inequality in Musielak- Orlicz spaces.

    DOI: 10.5186/aasfm.2016.4148

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  • Weighted variable modulation spaces 査読

    野井貴弘, 澤野嘉宏

    Sci. Math. Jpn.   79 ( 1 )   21 - 32   2016年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Hardy spaces with variable exponents on RD-spaces and applications 査読

    Ciqiang Zhuo, Yoshihiro Sawano, Dachun Yang

    DISSERTATIONES MATHEMATICAE   520 ( 520 )   1 - 74   2016年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN  

    In this article, the authors introduce Hardy spaces with variable exponents, H*(,p(.)) (chi), on RD-spaces with infinite measures via the grand maximal function. Then the authors characterize these spaces by means of the non-tangential maximal function or the dyadic maximal function. Characterizations in terms of atoms or Littlewood-Paley functions are also established. As applications, the authors prove an Olsen inequality for fractional integral operators and the boundedness of singular integral operators and quasi-Banach valued sublinear operators on these spaces. Finally, a duality theory of these spaces is developed.

    DOI: 10.4064/dm744-9-2015

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  • A note on the complex interpolation of Morrey spaces 招待 査読

    Denny Ivanal Hakim, 澤野嘉宏

    Linear and Nonlinear Analysis   2 ( 2 )   199 - 213   2016年

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    記述言語:英語   掲載種別:研究論文(国際会議プロシーディングス)  

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  • On the compactness of commutators for rough marcinkiewicz integral operators 査読

    Suzhen Mao, Yoshihiro Sawano, Huoxiong Wu

    Taiwanese Journal of Mathematics   19 ( 6 )   1777 - 1793   2015年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:MATHEMATICAL SOC REP CHINA  

    Let b ∈ BMO(Rn) and MΩ be the Marcinkiewicz integral operator with kernel (Formula Presented), where Ω is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn−1. In this paper, by means of Fourier transform estimates and approximation to the operator MΩ with integral operators having smooth kernels we show that if b ∈ CMO(Rn) and Ω satisfies a certain weak size condition, then the commutator MΩ, b = [b, MΩ] generated by b and MΩ is a compact operator on Lp(Rn) for some 1 < p < ∞.

    DOI: 10.11650/tjm.19.2015.5656

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  • A remark on two generalized Orlicz-Morrey spaces 査読

    Sadek Gala, Yoshihiro Sawano, Hitoshi Tanaka

    Journal of Approximation Theory   198   1 - 9   2015年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    There have been known two generalized Orlicz-Morrey spaces. One is defined earlier by Nakai and the other is by Sugano, the second and third authors. In this paper we investigate differences between these two spaces in some typical cases. The arguments rely upon property of the characteristic function of the Cantor set.

    DOI: 10.1016/j.jat.2015.04.001

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  • Non-smooth atomic decomposition for generalized Orlicz-Morrey spaces 査読

    Yoshihiro Sawano, Denny Ivanal Hakim, Hendra Gunawan

    Mathematische Nachrichten   288 ( 14-15 )   1741 - 1775   2015年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-V C H VERLAG GMBH  

    In the present paper, we consider the non-smooth atomic decomposition of generalized Orlicz-Morrey spaces. The result will be sharper than the existing results. As an application, we consider the boundedness of the bilinear operator, which is called the Olsen inequality nowadays. To obtain a sharp norm estimate, we first investigate their predual space, which is even new, and we make full advantage of the vector-valued inequality for the Hardy-Littlewood maximal operator.

    DOI: 10.1002/mana.201400138

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  • A unified treatment of Hilbert-type inequalities involving the Hardy operator 査読

    Tserendorj Batbold, Yoshihiro Sawano

    Mathematical Inequalities and Applications   18 ( 3 )   827 - 843   2015年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELEMENT  

    In this paper we shall provide a unified treatment of Hilbert-type inequalities involving the Hardy operator with a general homogeneous kernel. Furthermore, we establish some new Hilbert-type inequalities involving the integral operator. We shall show that the constants in our results are best possible.

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  • Littlewood–Paley theory for Morrey spaces and their preduals 査読

    Takashi Izumi, Yoshihiro Sawano, Hitoshi Tanaka

    Revista Matematica Complutense   28 ( 2 )   411 - 447   2015年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2014, Universidad Complutense de Madrid. Zorko proved that Morrey spaces are known to have preduals. In the present paper such predual spaces are shown to be characterized by means of the Littlewood–Paley operators. Recently, many function spaces are shown to admit the Littlewood–Paley characterization. As for the predual spaces of Morrey spaces, it had not been clear that a pointwise increasing norm-bounded sequence has a least bound. However, the author proved in the earlier paper that it actually has a least bound. In the present paper, by taking advantage of this property, a characterization by means of Littlewood–Paley operators is proposed.

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  • WAVELET CHARACTERIZATION AND MODULAR INEQUALITIES FOR WEIGHTED LEBESGUE SPACES WITH VARIABLE EXPONENT 査読

    Mitsuo Izuki, Eiichi Nakai, Yoshihiro Sawano

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA   40 ( 2 )   551 - 571   2015年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SUOMALAINEN TIEDEAKATEMIA  

    In this paper, we characterize weighted Lebesgue spaces with variable exponent in terms of wavelet. Also, we disprove some weighted modular inequalities when the exponent is not a constant one without using the A(infinity)-condition on weights. As a byproduct, we shall obtain the vector-valued maximal inequalities in the weighted setting.

    DOI: 10.5186/aasfm.2015.4032

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  • The Fatou property of block spaces 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Journal of Mathematical Sciences (Japan)   22 ( 3 )   663 - 683   2015年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Around thirty years ago, block spaces, which are the predual of Morrey spaces, had been considered. However, it seems that there is no proof that block spaces satisfy the Fatou property. In this paper the Fatou property for block spaces is verified and the predual of block spaces is characterized.

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  • Boundedness of intrinsic square functions and their commutators on generalized weighted orlicz-morrey spaces 査読

    Vagif Guliyev, Mehriban Omarova, Yoshihiro Sawano

    Banach Journal of Mathematical Analysis   9 ( 2 )   44 - 62   2015年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:TUSI MATHEMATICAL RESEARCH GROUP  

    We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces MΦω,α (Rn). In all the cases, the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on weights ' without assuming any monotonicity property of α(x,·) with x fixed.

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  • Sobolev embeddings for Riesz potentials of functions in Musielak–Orlicz–Morrey spaces over non-doubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Integral Transforms and Special Functions   25 ( 12 )   976 - 991   2014年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    © 2014, © 2014 Taylor &amp; Francis. In this paper we are concerned with Sobolev embeddings for Riesz potentials of functions in Musielak–Orlicz–Morrey spaces over non-doubling measure spaces. We deal with the boundedness of the generalized maximal operators, Sobolev&#039;s inequality, Trudinger&#039;s inequality and continuity for Riesz potentials of variable order. We prove the results in full generality: our function spaces will cover Morrey spaces, variable Lebesgue spaces as well as Lebesgue spaces with a Radon measure μ. Also, we can readily handle function spaces on metric measure spaces. Our results will cover the ones in our earlier paper [Sawano Y, Shimomura T. Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. Collect. Math. 2013;64:313–350]. We shall show that the Trudinger exponential integrability is available in our generalized setting, whose counterpart on Lebesgue spaces was not considered in Mizuta et al. [Maximal functions, Riesz potentials and Sobolev embeddings on Musielak–Orlicz–Morrey spaces of variable exponent in Rn. Rev. Mat. Complut. 2012;25:413–434.]

    DOI: 10.1080/10652469.2014.955099

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  • Variable Lebesgue norm estimates for BMO functions. II 査読

    Mitsuo Izuki, Yoshihiro Sawano, Yohei Tsutsui

    Analysis Mathematica   40 ( 3 )   215 - 230   2014年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AKADEMIAI KIADO RT  

    The paper concerns characterization of BMO in terms of Banach function spaces. In particular, we are interested in characterizing BMO by using the variable Lebesgue norm. © 2014 Akadémiai Kiadó, Budapest, Hungary.

    DOI: 10.1007/s10476-014-0304-6

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  • Approximation in Banach space by linear positive operators 査読

    Arash Ghorbanalizadeh, Yoshihiro Sawano

    Positivity   18 ( 3 )   585 - 594   2014年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    In this paper, we obtain a sufficient condition for the convergence of positive linear operators in Banach function spaces on ℝn and derive a Korovkin type theorem for these spaces. Also, we generalized this result via statistical sense. © 2013 Springer Basel.

    DOI: 10.1007/s11117-013-0264-2

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  • Orlicz-Hardy spaces and their duals 査読

    Eiichi Nakai, Yoshihiro Sawano

    Science China Mathematics   57 ( 5 )   903 - 962   2014年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SCIENCE PRESS  

    We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions. The class will be wider than the class of all the N-functions. In particular, we consider the non-smooth atomic decomposition. The relation between Orlicz-Hardy spaces and their duals is also studied. As an application, duality of Hardy spaces with variable exponents is revisited. This work is different from earlier works about Orlicz-Hardy spaces H Φ(ℝn) in that the class of admissible functions φ is largely widened. We can deal with, for example, with p 1, p 2 ∈ (0,∞) and q 1, q 2 ∈ (-∞,∞), where we shall establish the boundedness of the Riesz transforms on H Φ(ℝn). In particular, φ{symbol} is neither convex nor concave when 0 < p 1 < 1 < p 2 < ∞, 0 < p 2 < 1 < p 1 < ∞ or p 1 = p 2 = 1 and q 1, q 2 > 0. If Φ(r) ≡ r(log(e+r))q, then H Φ(ℝn) = H(log H)q(ℝn). We shall also establish the boundedness of the fractional integral operators I α of order α ∈ (0,∞). For example, I α is shown to be bounded from H(log H)1 - α/n (ℝn) to L n/(n - α)(log L)(ℝn) for 0 < α < n. © 2014 Science China Press and Springer-Verlag Berlin Heidelberg.

    DOI: 10.1007/s11425-014-4798-y

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  • Morrey-type spaces on gauss measure spaces and boundedness of singular integrals 査読

    Liguang Liu, Yoshihiro Sawano, Dachun Yang

    Journal of Geometric Analysis   24 ( 2 )   1007 - 1051   2014年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    In this paper, the authors introduce Morrey-type spaces on the locally doubling metric measure spaces, which means that the underlying measure enjoys the doubling and the reverse doubling properties only on a class of admissible balls, and then obtain the boundedness of the local Hardy-Littlewood maximal operator and the local fractional integral operator on such Morrey-type spaces. These Morrey-type spaces on the Gauss measure space are further proved to be naturally adapted to singular integrals associated with the Ornstein-Uhlenbeck operator. To be precise, by means of the locally doubling property and the geometric properties of the Gauss measure, the authors establish the equivalence between Morrey-type spaces and Campanato-type spaces on the Gauss measure space, and the boundedness for a class of singular integrals associated with the Ornstein-Uhlenbeck operator (including Riesz transforms of any order) on Morrey-type spaces over the Gauss measure space. © 2012 Mathematica Josephina, Inc.

    DOI: 10.1007/s12220-012-9362-9

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  • Characterizations for the generalized fractional integral operators on morrey spaces 査読

    Eridani, Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano

    Mathematical Inequalities and Applications   17 ( 2 )   761 - 777   2014年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ELEMENT  

    We present some characterizations for the boundedness of the generalized fractional integral operators on Morrey spaces. The characterizations follow from two key estimates, one for the norm of some functions in Morrey spaces, and another for the values of the corresponding fractional integrals. We prove three theorems about necessary and sufficient conditions. We show that these theorems are independent by giving some examples. We also obtain counterparts for the weak generalized Morrey spaces.

    DOI: 10.7153/mia-17-56

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  • Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz-Morrey spaces 査読

    Sadek Gala, Maria Alessandra Ragusa, Yoshihiro Sawano, Hitoshi Tanaka

    Applicable Analysis   93 ( 2 )   356 - 368   2014年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:TAYLOR & FRANCIS LTD  

    Consider the quasi-geostrophic equations with the initial data. Let and be two weak solutions with the same initial value. If where is the Orlicz-Morrey space (for a definition of this space, see Definition), then we have. In view of the embedding with and, we see that our result improves the previous result of Dong and Chen. This is an extension of earlier regularity results in the Serrin's type space. © 2013 © 2013 Taylor & Francis.

    DOI: 10.1080/00036811.2013.772582

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  • A new Brézis-Gallouët-Wainger inequality from the viewpoint of the real interpolation functors 査読

    Yoshihiro Sawano

    Mathematische Nachrichten   287 ( 2-3 )   352 - 358   2014年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    The Brézis-Gallouët-Wainger inequality describes a subtle embedding property into L∞. The relation between the Brézis-Gallouët-Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between L∞ and the logarithmic boundedness, which is supposed to be the right-hand side of the Brézis-Gallouët-Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem. © 2013 WILEY-VCH Verlag GmbH &amp; Co. KGaA, Weinheim.

    DOI: 10.1002/mana.201100324

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  • Fatou property of predual Morrey spaces with non-doubling measures 査読

    田中仁, 澤野嘉宏

    Int. J. Appl. Math.   27 ( 3 )   283 - 296   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Fractional type Marcinkiewicz integral operators associated to surfaces 査読

    Yoshihiro Sawano, Kôzô Yabuta

    Journal of Inequalities and Applications   2014 ( 1 )   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Springer International Publishing  

    In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and we extend a result given by Chen et al. (J. Math. Anal. Appl. 276:691-708, 2002). They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces (Formula presented.) to (Formula presented.). Recently the second author, together with Xue and Yan, greatly weakened their assumptions. In this paper, we extend their results to the case where the operators are associated to the surfaces of the form (Formula presented.). To prove our result, we discuss a characterization of the homogeneous Triebel-Lizorkin spaces in terms of lacunary sequences.

    DOI: 10.1186/1029-242X-2014-232

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  • Decompositions for local morrey spaces 査読

    Tserendorj Batbold, Yoshihiro Sawano

    Eurasian Mathematical Journal   5 ( 3 )   9 - 45   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We develop and apply a decomposition theory for generic local Morrey spaces. Our results are smooth and nonsmooth decompositions, which follows from the fact that local Morrey spaces are isomorphic to local Hardy-Morrey spaces and local Triebel-Lizorkin-Morrey spaces in the generic case. As an application of our results, we consider a bilinear estimate for the fractional integral operators.

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  • Atomic decomposition for Morrey spaces 査読

    Takeshi Iida, Yoshihiro Sawano, Hitoshi Tanaka

    Zeitschrift fur Analysis und ihre Anwendung   33 ( 2 )   149 - 170   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:EUROPEAN MATHEMATICAL SOC  

    The Hardy space Hp(ℝn) substitutes for the Lebesgue space Lp(ℝn). When p > 1, then the Hardy space Hp(ℝn) coincides with the Lebesgue spaces Lp(ℝn). This is shown by using the reexivity of the function spaces. The atomic decomposition is readily available for H p(ℝn) with 0 < p < ∞. This idea can be applied to many function spaces. As example of such an attempt, we now propose here a non-smooth decomposition of Morrey spaces. As applications, we consider the Olsen inequality. In the end of this article, we compare our results with existing ones and propose some possibility of extensions, which are left as future works. © European Mathematical Society.

    DOI: 10.4171/ZAA/1504

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  • Morrey spaces and related function spaces 招待

    Yoshihiro Sawano, Hendra Gunawan, Vagif Guliyev, Hitoshi Tanaka

    Journal of Function Spaces   2014   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:HINDAWI PUBLISHING CORPORATION  

    DOI: 10.1155/2014/867192

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  • Function spaces with variable exponents--an introduction-- 査読

    出来光夫, 中井英一, 澤野嘉宏

    Sci. Math. Jpn.   77 ( 2 )   187 - 315   2014年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Collectanea Mathematica   64 ( 3 )   313 - 350   2013年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER-VERLAG ITALIA SRL  

    The target is potential theory in connection with Morrey spaces on general metric measure spaces. The present paper is oritented to investigating Sobolev's inequality, Trudinger exponential integrability and continuity for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. A counterexample shows that our results are reasonable. In addition to the example above, what is new about this paper is that everything can be developed once the underlying measure does not charge any point. © 2013 The Author(s).

    DOI: 10.1007/s13348-013-0082-7

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  • Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators 査読

    Yoshihiro Sawano

    Integral Equations and Operator Theory   77 ( 1 )   123 - 148   2013年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    As applications of atomic decomposition results of Hardy spaces with variable exponents, we shall prove the boundedness of commutators and the fractional integral operators as well as the Hardy operators. There are many ways to prove such boundedness. For example, the boundedness of commutators can be proved by the sharp maximal inequalities. But here, we propose a different method based upon our atomic decomposition. © 2013 Springer Basel.

    DOI: 10.1007/s00020-013-2073-1

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  • A criterion of sampling theorems on banach function spaces 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Tokyo Journal of Mathematics   36 ( 1 )   269 - 287   2013年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In the present paper, we consider sampling theorems on Banach function spaces. Here we obtain a necessary and sufficient condition. For the latter half of the paper, we consider sampling theorems in terms of wavelets.

    DOI: 10.3836/tjm/1374497524

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  • On the uniqueness of weak solutions of the 3D MHD equations in the Orlicz-Morrey space 査読

    Sadek Gala, Yoshihiro Sawano, Hitoshi Tanaka

    Applicable Analysis   92 ( 4 )   776 - 783   2013年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:TAYLOR & FRANCIS LTD  

    In this article, we show that if a Leray solution (u, b) to the 3D magneto-hydrodynamic equation belongs to L2/1-r((0,T);M3/rL2logPL(ℝ3)), with r ∈ (0, 1) and P > 1, then (u, b) is the unique Leray solution on (0, T). © 2013 Copyright Taylor and Francis Group, LLC.

    DOI: 10.1080/00036811.2011.636357

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  • On the Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space 査読

    Yoshihiro Sawano, Hidemitsu Wadade

    Journal of Fourier Analysis and Applications   19 ( 1 )   20 - 47   2013年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Our main purpose in this article is to establish a Gagliardo-Nirenberg type inequality in the critical Sobolev-Morrey space HMn/pp,q(ℝn) with n∈ℕ and 1<q≤p<∞, which coincides with the usual critical Sobolev space HMn/pp,q(ℝn in the case of q=p. Indeed, we shall show the following interpolation inequality. If q<p, there exists a positive constant Cp,q depending only on p and q such that for all u∈HMn/pp,q(ℝn) and for all p≤r<∞. In the case of q=p, that is, the case of the critical Sobolev space, the corresponding inequality was obtained in Ogawa (Nonlinear Anal. 14:765-769, 1990), Ogawa-Ozawa (J. Math. Anal. Appl. 155:531-540, 1991) and Ozawa (J. Func. Anal. 127:259-269, 1995) with the growth order r1-1/p as r→∞. The inequality (GN) implies that the growth order as r→∞ is linear, which might look worse compared to the case of the critical Sobolev space. However, we investigate the optimality of the growth order and prove that this linear order is best-possible. Furthermore, as several applications of the inequality (GN), we shall obtain a Trudinger-Moser type inequality and a Brézis-Gallouët-Wainger type inequality in the critical Sobolev-Morrey space. © 2012 Springer Science+Business Media, LLC.

    DOI: 10.1007/s00041-012-9223-8

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  • Integral operators on B<inf>σ</inf>-Morrey-Campanato spaces 査読

    Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai, Yoshihiro Sawano

    Revista Matematica Complutense   26 ( 1 )   1 - 32   2013年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We show the boundedness of the Hardy-Littlewood maximal operator, singular and fractional integral operators, and more general sublinear operators on Bσ-Morrey-Campanato spaces. These function spaces have been introduced recently to unify central Morrey spaces, λ-central mean oscillation spaces and usual Morrey-Campanato spaces. Using the Bσ-Morrey-Campanato spaces, we can study both local and global regularities of functions simultaneously, and unify a series of results on the boundedness of operators on several classical function spaces. © 2011 Revista Matemática Complutense.

    DOI: 10.1007/s13163-011-0091-6

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  • Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Journal of Inequalities and Applications   2013   1 - 19   2013年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER INTERNATIONAL PUBLISHING AG  

    Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces. The main result is oriented to the outrange of the well-known Adams theorem. © 2013 Sawano and Shimomura; licensee Springer.

    DOI: 10.1186/1029-242X-2013-12

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  • Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Journal of Inequalities and Applications   2013   2013年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces. The main result is oriented to the outrange of the well-known Adams theorem. © 2013 Sawano and Shimomura
    licensee Springer.

    DOI: 10.1186/1029-242X-2013-12

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  • Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials 査読

    Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano, Tetsu Shimomura

    Journal of the Mathematical Society of Japan   65 ( 2 )   633 - 670   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:MATH SOC JAPAN  

    Our aim in this paper is to prove the Gagliardo-Nirenberg inequality for Riesz potentials of functions in variable exponent Lebesgue spaces, which are called Musielak-Orlicz spaces with respect to Φ(x, t) = t p(x)(log(c0 + t))q(x) for t > 0 and x ε ℝn, via the Littlewood-Paley decomposition. © 2013 The Mathematical Society of Japan.

    DOI: 10.2969/jmsj/06520633

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  • Martingale Morrey-Hardy and campanato-hardy spaces

    Eiichi Nakai, Gaku Sadasue, Yoshihiro Sawano

    Journal of Function Spaces and Applications   2013   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:HINDAWI PUBLISHING CORPORATION  

    We introduce generalized Morrey-Campanato spaces of martingales, which generalize both martingale Lipschitz spaces introduced by Weisz (1990) and martingale Morrey-Campanato spaces introduced in 2012. We also introduce generalized Morrey-Hardy and Campanato-Hardy spaces of martingales and study Burkholder-type equivalence. We give some results on the boundedness of fractional integrals of martingales on these spaces. © 2013 Eiichi Nakai et al.

    DOI: 10.1155/2013/690258

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  • Characterization of the multipliers from Ḣr to Ḣ-r 査読

    Sadek Gala, Yoshihiro Sawano

    Bulletin of the Korean Mathematical Society   50 ( 3 )   915 - 928   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In this paper, we will provide an alternative proof to characterize the pointwise multipliers which maps a Sobolev space Ḣr (ℝd) to its dual Ḣr (ℝd) in the case 0 &lt; r &lt; d2 by a simple application of the definition of fractional Sobolev space. The proof relies on a method introduced by Maz&#039;ya-Verbitsky [9] to prove the same result. © 2013 The Korean Mathematical Society.

    DOI: 10.4134/BKMS.2013.50.3.915

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  • A new framework for generalized Besov-type and Triebel?Lizorkin-type spaces 査読

    Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich

    Dissertationes Mathematicae   ( 489 )   5 - 114   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN  

    In this paper, the authors propose a new framework under which a theory of generalized Besovtype and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is an application of the Peetre maximal function. This idea originates from recen fndings in the abstract coorbit space theory obtained by Holger Rauhut and Tino Ullrich. In this new setting, the authors establish the boundedness of pseudo-differential operators based on atomic and molecular characterizations and also the boundedness of Fourier multipliers. Characterizations of these function spaces by means of differences and oscillations are also established. As further applications of this new framework, the authors reexamine and polish some existing results for many different scales of function spaces.

    DOI: 10.4064/dm489-0-1

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  • A note on the boundedness of discrete commutators on Morrey spaces and their preduals 査読

    Y. Sawano

    Journal of Analysis and Applications   11 ( 1 )   1 - 26   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Dyadic fractional integral operators are shown to be bounded on Morrey spaces and their preduals. It seems that the proof of the boundedness by means of dyadic fractional integral operators is effective particularly on the preduals. In the present paper the commutators are proved to be bounded as well. © SAS International Publications.

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  • Linear and sublinear operators on generalized Morrey spaces with non-doubling measures 査読

    Vagif Guliyev, Yoshihiro Sawano

    Publicationes Mathematicae   83 ( 3 )   303 - 327   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:KOSSUTH LAJOS TUDOMANYEGYETEM  

    By using a geometric structure of the Euclidean space, the theory of generalized Morrey spaces is shown to be available in the non-doubling setting. Some classical operators are established to be bounded in the generalized spaces defined in the present paper.

    DOI: 10.5486/PMD.2013.5508

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  • Applications of Littlewood-Paley Theory for (B) over dot(sigma)-Morrey Spaces to the Boundedness of Integral Operators 査読

    Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai, Yoshihiro Sawano

    JOURNAL OF FUNCTION SPACES AND APPLICATIONS   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:HINDAWI PUBLISHING CORPORATION  

    The boundedness of the various operators on (B) over dot(sigma)-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization of (B) over dot(sigma)-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization of (B) over dot(sigma)-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators on (B) over dot(sigma)-Lipschitz spaces is discussed.

    DOI: 10.1155/2013/859402

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  • Applications of Littlewood-Paley theory for B ̇ σ-Morrey spaces to the boundedness of integral operators 査読

    Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai, Yoshihiro Sawano

    Journal of Function Spaces and Applications   2013   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    The boundedness of the various operators on B ̇ σ -Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization of B ̇ σ -Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization of B ̇ σ -Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators on B ̇ σ -Lipschitz spaces is discussed. © 2013 Yasuo Komori-Furuya et al.

    DOI: 10.1155/2013/859402

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  • Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces 査読

    Idha Sihwaningrum, 澤野嘉宏

    Eurasian Math. J.   4 ( 1 )   76 - 81   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces 査読

    Hendra Gunawan, Denny Ivanal Hakim, Yoshihiro Sawano, Idha Sihwaningrum

    JOURNAL OF FUNCTION SPACES AND APPLICATIONS   2013   1 - 12   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:HINDAWI PUBLISHING CORPORATION  

    We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

    DOI: 10.1155/2013/809704

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  • Hardy spaces with variable exponent 査読

    出耒 光夫, 中井 英一, 澤野嘉宏

    RIMS Kokyuroku Bessatsu   B42   109 - 136   2013年

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    記述言語:英語   出版者・発行元:京都大学  

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  • The Hardy-Littlewood maximal operator on Lebesgue spaces with variable exponent 査読

    出耒 光夫, 中井 英一, 澤野嘉宏

    RIMS Kokyuroku Bessatsu   B42   51 - 94   2013年

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    記述言語:英語   出版者・発行元:京都大学  

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  • Sobolev embeddings for generalized riesz potentials of functions in morrey spaces L(1, φ)(G) over nondoubling measure spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Journal of Function Spaces and Applications   2013   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    Our aim in this paper is to deal with the Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces L(1, φ)(G) over nondoubling measure spaces. © 2013 Yoshihiro Sawano and Tetsu Shimomura.

    DOI: 10.1155/2013/984259

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  • Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces over Nondoubling Measure Spaces 査読

    Yoshihiro Sawano, Tetsu Shimomura

    Journal of Function Spaces and Applications   2013   1 - 12   2013年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Hindawi Publishing Corporation  

    Our aim in this paper is to deal with the Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces L-(1,L-phi)(G) over nondoubling measure spaces.

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  • New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets 査読

    Yiyu Liang, Yoshihiro Sawano, Tino Ullrich, Dachun Yang, Wen Yuan

    Journal of Fourier Analysis and Applications   18 ( 5 )   1067 - 1111   2012年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER BIRKHAUSER  

    In this paper, the authors establish new characterizations of the recently introduced Besov-type spaces B S,τp,q(ℝ n) and Triebel-Lizorkin-type spaces F S,τp,q(ℝ n) with p∈(0,∞], s∈ℝ, τ∈[0,∞), and q∈(0,∞], as well as their preduals, the Besov-Hausdorff spaces BH S,τp,q(ℝ n) and Triebel-Lizorkin-Hausdorff spaces FH S,τp,q(ℝ n), in terms of the local means, the Peetre maximal function of local means, and the tent space (the Lusin area function) in both discrete and continuous types. As applications, the authors then obtain interpretations as coorbits in the sense of Rauhut (Stud. Math. 180:237-253, 2007) and discretizations via biorthogonal wavelet bases for the full range of parameters of these function spaces. Even for some special cases of this setting such as F S∞,q(ℝ n) for s∈ℝ, q∈(0,∞] (including BMO(ℝ n) when s=0 and q=2), the Q space Q α(ℝ n), the Hardy-Hausdorff space HH -α(ℝ n) for α∈(0,min{n/2,1}), the Morrey space M up(ℝ n) for 1 < p ≤ u < ∞, and the Triebel-Lizorkin-Morrey space E Supq(ℝ n) for 0 < p ≤ u < ∞, s ∈ ℝ and q∈(0,∞], some of these results are new. © 2012 Springer Science+Business Media, LLC.

    DOI: 10.1007/s00041-012-9234-5

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  • Variable Lebesgue norm estimates for BMO functions 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Czechoslovak Mathematical Journal   62 ( 3 )   717 - 727   2012年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER HEIDELBERG  

    In this paper, we are going to characterize the space BMO(ℝ n) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO(ℝ n) by using various function spaces. For example, Ho obtained a characterization of BMO(ℝ n) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue of the well-known John-Nirenberg inequality which can be seen as an extension to the variable Lebesgue spaces. © 2012 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.

    DOI: 10.1007/s10587-012-0042-5

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  • A new Beale-Kato-Majda criteria for the 3D magneto-micropolar fluid equations in the Orlicz-Morrey space 査読

    Sadek Gala, Yoshihiro Sawano, Hitoshi Tanaka

    Mathematical Methods in the Applied Sciences   35 ( 11 )   1321 - 1334   2012年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-BLACKWELL  

    In this work, we are interested in the study of regularity for the three-dimensional magneto-micropolar fluid equations in Orlicz-Morrey spaces. If the velocity field satisfies u∈L21-r0,T;ML2logPL3rR3 with r∈(0,1) and P>1 or the gradient field of velocity satisfies ∇u∈L22-r0, T;ML2logPL3rR3 with r∈(0,2) and P>1, then we show that the solution remains smooth on [0,T]. In view of the embedding L3r⊂Mp3r⊂ML2logPL3r with 2 < p < 3 / r and P > 1, we see that our result extends the result of Yuan and that of Gala. Copyright © 2012 John Wiley & Sons, Ltd.

    DOI: 10.1002/mma.2535

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  • Multilinear fractional integrals on Morrey spaces 査読

    Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka

    Acta Mathematica Sinica, English Series   28 ( 7 )   1375 - 1384   2012年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER HEIDELBERG  

    In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality. © 2012 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.

    DOI: 10.1007/s10114-012-0617-y

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  • Sharp bounds for multilinear fractional integral operators on Morrey type spaces

    Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka

    Positivity   16 ( 2 )   339 - 358   2012年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    A multi-Morrey norm which is strictly smaller than m-fold product of the Morrey norms is introduced and the boundedness property of the Adams type for multilinear fractional integral operators is obtained. The optimality of the results is also discussed. © 2011 Springer Basel AG.

    DOI: 10.1007/s11117-011-0129-5

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  • Hardy spaces with variable exponents and generalized Campanato spaces 査読

    Eiichi Nakai, Yoshihiro Sawano

    Journal of Functional Analysis   262 ( 9 )   3665 - 3748   2012年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In the present paper we define Hardy spaces with variable exponents on Rn by the grand maximal function, and then investigate their several properties. The present paper will connect harmonic analysis with function spaces with variable exponents. We obtain the atomic decomposition and the molecular decomposition. With these decomposition proved, we investigate the Littlewood-Paley characterization. Also, we specify the dual spaces of Hardy spaces with variable exponents. They will turn out to be Campanato spaces with variable growth conditions. The present paper covers local Hardy spaces with variable exponents. © 2012 Elsevier Inc.

    DOI: 10.1016/j.jfa.2012.01.004

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  • Orlicz-Morrey Spaces and Fractional Operators 査読

    Yoshihiro Sawano, Satoko Sugano, Hitoshi Tanaka

    Potential Analysis   36 ( 4 )   517 - 556   2012年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER  

    By taking an interest in a natural extension to the small parameters of the trace inequality for Morrey spaces, Orlicz-Morrey spaces are introduced and some inequalities for generalized fractional integral operators on Orlicz-Morrey spaces are established. The local boundedness property of the Orlicz maximal operators is investigated and some Morrey-norm equivalences are also verified. The result obtained here sharpens the one in our earlier papers. © 2011 Springer Science+Business Media B.V.

    DOI: 10.1007/s11118-011-9239-8

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  • Complex interpolation of Besov spaces and Triebel-Lizorkin spaces with variable exponents 査読

    Takahiro Noi, Yoshihiro Sawano

    Journal of Mathematical Analysis and Applications   387 ( 2 )   676 - 690   2012年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    This paper concerns the complex interpolation of Besov spaces and Triebel-Lizorkin spaces with variable exponents. © 2011 Elsevier Inc.

    DOI: 10.1016/j.jmaa.2011.09.023

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  • Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces 査読

    Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano, Tetsu Shimomura

    Archiv der Mathematik   98 ( 3 )   253 - 263   2012年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:BIRKHAUSER VERLAG AG  

    The aim of this paper is to give a Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over spaces of homogeneous type. © 2012 Springer Basel AG.

    DOI: 10.1007/s00013-012-0362-6

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  • General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces 査読

    L. P. Castro, S. Saitoh, Y. Sawano, A. M. Simões

    Complex Analysis and Operator Theory   6 ( 1 )   307 - 324   2012年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:BIRKHAUSER VERLAG AG  

    In this paper we shall introduce new constructions of approximate solutions of general linear partial differential equations with constant coefficients on the whole spaces, and establish fundamental estimates of the solutions depending on the inhomogeneous terms. This will be done by combining general ideas of the Tikhonov regularization and discretization of bounded linear operator equations on reproducing kernel Hilbert spaces. Furthermore, we will provide approximate solutions for the related inverse source problems. © 2010 Springer Basel AG.

    DOI: 10.1007/s11785-010-0083-4

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  • Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Mathematische Nachrichten   285 ( 1 )   103 - 126   2012年1月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-BLACKWELL  

    Rychkov defined weighted Besov spaces and weighted Triebel-Lizorkin spaces coming with a weight in the class Aploc, which is even wider than the class Ap due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

    DOI: 10.1002/mana.200910201

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  • Fractional integral operators in generalized Morrey spaces defined on metric measure spaces 査読

    Eridani, 澤野嘉宏

    Proceeding of A. Razmadze Mathematical Institute   158   13 - 24   2012年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Lower bound for sharp constants of Brézis-Gallouët-Wainger type inequalities in higher-order critical sobolev spaces on bounded domains 査読

    Kei Morii, Y. Sawano

    Communications in Mathematical Analysis   12 ( 1 )   1 - 16   2012年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    As an application of our previous paper, we give a sufficient condition that Brézis- Gallouët-Wainger type inequalities in higher order critical Sobolev spaces fails.

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  • Discrete linear differential equations 査読

    Luis P. Castro, Saburou Saitoh, Anabela S. Silva, Yoshihiro Sawano

    Analysis (Germany)   32 ( 3 )   181 - 191   2012年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We propose new constructions of the approximate solutions of discrete linear differential equations and their inverse source problems. This is mainly based on a reproducing kernel Hilbert spaces approach where different types of spaces are naturally considered as a consequence of the method. Here, the major influence will be given by the Paley-Wiener and Sobolev spaces. © 2012, by Oldenbourg Wissenschaftsverlag, München, Germany. All rights reserved.

    DOI: 10.1524/anly.2012.1104

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  • Fundamental error estimate inequalities for the tikhonov regularization using reproducing kernels

    Luís P. Castro, Hiroshi Fujiwara, Saburou Saitoh, Yoshihiro Sawano, Akira Yamada, Masato Yamada

    International Series of Numerical Mathematics   161   87 - 101   2012年

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    掲載種別:論文集(書籍)内論文  

    First of all, we will be concentrated in some particular but very important inequalities. Namely, for a real-valued absolutely continuous function on [0,1], satisfying f(0)=0 and $\int:{0}^{1}f'(x)^{2}\,dx<1$, we have, by using the theory of reproducing kernels $$\int:0^1\left(\frac{f(x)}{1-f(x)}\right)^{\prime\,2}(1-x)^2\,dx \le\frac{\int_0^1f^{\prime\,2}(x)\,dx}{1-\int_0^1f^{\prime\,2}(x)\,dx}. $$ A. Yamada gave a direct proof for this inequality with a generalization and, as an application, he unified the famous Opial inequality and its generalizations. Meanwhile, we gave some explicit representations of the solutions of nonlinear simultaneous equations and of the explicit functions in the implicit function theory by using singular integrals. In addition, we derived estimate inequalities for the consequent regularizations of singular integrals. Our main purpose in this paper is to introduce our method of constructing approximate and numerical solutions of bounded linear operator equations on reproducing kernel Hilbert spaces by using the Tikhonov regularization. In view of this, for the error estimates of the solutions, we will need the inequalities for the approximate solutions. As a typical example, we shall present our new numerical and real inversion formulas of the Laplace transform whose problems are famous as typical ill-posed and difficult ones. In fact, for this matter, a software realizing the corresponding formulas in computers is now included in a present request for international patent. Here, we will be able to see a great computer power of H. Fujiwara with infinite precision algorithms in connection with the error estimates.

    DOI: 10.1007/978-3-0348-0249-9_6

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  • Generalized stummel class and morrey spaces 査読

    Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano, Hitoshi Tanaka

    Publications de l'Institut Mathematique   92 ( 106 )   128 - 137   2012年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:PUBLICATIONS L INSTITUT MATHEMATIQUE MATEMATICKI  

    We revisit the Stummel class and its relation with Morrey spaces. We reformulate a result of Ragusa and Zamboni [11] and then discuss its generalization, as proposed by Eridani and Gunawan [4]. An improvement of the results previously obtained by Eridani and Gunawan is obtained and some extensions are presented.

    DOI: 10.2298/PIM1206127G

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  • Application of reproducing kernel Hilbert spaces to a minimization problem with prescribed nodes 査読

    Hendra Gunawan, Yoshihiro Sawano

    East Asian Journal on Applied Mathematics   1 ( 4 )   372 - 378   2011年11月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:GLOBAL SCIENCE PRESS  

    The theory of reproducing kernel Hilbert spaces is applied to a minimization problem with prescribed nodes. We re-prove and generalize some results previously obtained by Gunawan et al. [2,3], and also discuss the Hölder continuity of the solution to the problem. © 2011 Global-Science Press.

    DOI: 10.4208/eajam.050511.310711a

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  • Pasting reproducing kernel Hilbert spaces 査読

    Yoshihiro Sawano

    Jaen Journal on Approximation   3 ( 1 )   135 - 141   2011年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In the present paper, two new operation on reproducing kernel Hilbert spaces are proposed. One is the pasting and another is the wedge product. As applications of these operations, we reconsider the Cauchy-Binet formula. © 2011 Universidad de Jaén.

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  • Generalized fractional integral operators and fractional maximal operators in the framework of morrey spaces 査読

    Yoshihiro Sawano, Satoko Sugano, Hitoshi Tanaka

    Transactions of the American Mathematical Society   363 ( 12 )   6481 - 6503   2011年7月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under point wise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The bounded ness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the Fefferman-Phong inequality is given by the use of the characteristic function of the Cantor set. © 2011 American Mathematical Society.

    DOI: 10.1090/S0002-9947-2011-05294-3

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  • Weighted norm inequalities for multilinear fractional operators on Morrey spaces 査読

    Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka

    Studia Mathematica   205 ( 2 )   139 - 170   2011年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS  

    A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered. © Instytut Matematyczny PAN, 2011.

    DOI: 10.4064/sm205-2-2

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  • Molecular decomposition of the modulation spaces 査読

    Masaharu Kobayashi, Yoshihiro Sawano

    Osaka Journal of Mathematics   47 ( 4 )   1029 - 1053   2010年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:OSAKA JOURNAL OF MATHEMATICS  

    The aim of this paper is to develop a theory of decomposition in the weighted modulation spaces Ms,Wp,q with 0 < p, q ≤ ∞, s ε R and W ε A∞, where W belongs to the class of A∞ defined by Muckenhoupt. For this purpose we shall define molecules for the modulation spaces. As an application we give a simple proof of the boundedness of the pseudo-differential operators with symbols in M∞0,min(1, p,q). We shall deal with dual spaces as well.

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  • Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains 査読

    Yoshihiro Sawano

    Mathematische Nachrichten   283 ( 10 )   1456 - 1487   2010年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-BLACKWELL  

    The purpose of this paper is to develop a theory of the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces on domains in Rn. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains in Rn we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p, q in the Morrey space Mpq. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

    DOI: 10.1002/mana.200710151

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  • Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications 査読

    Wen Yuan, Yoshihiro Sawano, Dachun Yang

    Journal of Mathematical Analysis and Applications   369 ( 2 )   736 - 757   2010年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let p∈(1,∞), q∈[1,∞), s∈R and τ∈[0,1- 1/max{p,q}]. In this paper, the authors establish the φ-transform characterizations of Besov-Hausdorff spaces BḢp,qs,τ(Rn) and Triebel-Lizorkin-Hausdorff spaces FḢp,qs,τ(Rn) (q>1); as applications, the authors then establish their embedding properties (which on BH p,qs,τ(Rn) is also sharp), smooth atomic and molecular decomposition characterizations for suitable τ. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in BḢp,qs,τ(Rn) and FḢp,qs,τ(Rn) (q>1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p∈(1,∞) and q∈[1,∞) by taking τ=0. © 2010 Elsevier Inc.

    DOI: 10.1016/j.jmaa.2010.04.021

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  • Maximal operator for Pseudodifferential operators with homogeneous symbols 査読

    Yoshihiro Sawano

    Michigan Mathematical Journal   59 ( 1 )   119 - 142   2010年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:MICHIGAN MATHEMATICAL JOURNAL  

    DOI: 10.1307/mmj/1272376028

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  • Singular integral inequalities and natural regularizations 査読

    Yoshihiro Sawano, Masato Yamada, Saburou Saitoh

    Mathematical Inequalities and Applications   13 ( 2 )   289 - 303   2010年4月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Element D.O.O.  

    We shall introduce natural regularizations for singular integrals from the viewpoint of numerical treatments and establish very good error estimates (fundamental inequalities for potentials) for the regularizations. © ELEMENT Zagreb.

    DOI: 10.7153/mia-13-23

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  • New applications of Besov-type and Triebel-Lizorkin-type spaces 査読

    Yoshihiro Sawano, Dachun Yang, Wen Yuan

    Journal of Mathematical Analysis and Applications   363 ( 1 )   73 - 85   2010年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper, the authors prove that Besov-Morrey spaces are proper subspaces of Besov-type spaces over(B, ̇)p, qs, τ (Rn) and that Triebel-Lizorkin-Morrey spaces are special cases of Triebel-Lizorkin-type spaces over(F, ̇)p, qs, τ (Rn). The authors also establish an equivalent characterization of over(B, ̇)p, qs, τ (Rn) when τ ∈ [0, 1 / p). These Besov-type spaces over(B, ̇)p, qs, τ (Rn) and Triebel-Lizorkin-type spaces over(F, ̇)p, qs, τ (Rn) were recently introduced to connect Besov spaces and Triebel-Lizorkin spaces with Q spaces. Moreover, for the spaces over(B, ̇)p, qs, τ (Rn) and over(F, ̇)p, qs, τ (Rn), the authors investigate their trace properties and the boundedness of the pseudo-differential operators with homogeneous symbols in these spaces, which generalize the corresponding classical results of Jawerth and Grafakos-Torres by taking τ = 0. © 2009 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2009.08.002

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  • The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Journal of Mathematical Analysis and Applications   362 ( 1 )   140 - 155   2010年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper we consider the Haar wavelet on weighted Herz spaces. Our weight class, whose name is Ap-dyadic local, is the one defined by the first author (2007). We shall investigate the class of Ap-dyadic weights in connection with the maximal inequalities. After obtaining the properties of weights in the first half of the present paper, we consider the Haar wavelet on weighted Herz spaces in the latter half. We shall show that the Haar wavelet basis is an unconditional basis. We also show that the Haar wavelet is not greedy except for the trivial case, that is, the Haar wavelet is greedy if and only if the Herz space under consideration is a weighted Lp space. © 2009 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2009.08.005

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  • Sharp constants of Brézis-Gallouët-Wainger type inequalities with a double logarithmic term on bounded domains in Besov and Triebel-Lizorkin spaces 査読

    Yoshihiro Sawano, Kei Morii, Tokushi Sato, Hidemitsu Wadade

    Boundary Value Problems   2010   2010年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding W1,n (ℝn) → L ∞(ℝn) fails for n≥2. Brézis- Gallouët-Wainger and some other authors quantified why this embedding fails by means of the Hlder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces. Copyright © 2010 Kei Morii et al.

    DOI: 10.1155/2010/584521

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  • Wavelet characterization of the pointwise multiplier space X<inf>r</inf> 査読

    Sadek Gala, Yoshihiro Sawano

    Functiones et Approximatio, Commentarii Mathematici   43 ( 2 )   109 - 116   2010年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Adam Mickiewicz University Press  

    In the present note we characterize the function space Xr, which is the set of pointwise multipliers which map L2 into H-r. To this end, we use wavelets and capacity.

    DOI: 10.7169/facm/1291903392

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  • Modulation spaces with A∞ weights 査読

    澤野嘉宏

    Cubo   12 ( 3 )   187 - 202   2010年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Certain identitieson derivatives of radial homogeneous and logarithmic functions 査読

    森井慶, 佐藤得志, 澤野嘉宏

    Communications in Mathematical Analysis   9 ( 2 )   51 - 66   2010年

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  • Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces 査読

    Yoshihiro Sawano

    Studia Mathematica   196 ( 1 )   91 - 101   2010年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp. © Instytut Matematyczny PAN, 2010.

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  • Greedy bases in weighted modulation spaces 招待 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Nonlinear Analysis, Theory, Methods and Applications   71 ( 12 )   E2045 - E2053   2009年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:PERGAMON-ELSEVIER SCIENCE LTD  

    In the present paper we consider weighted modulation spaces. Weights of exponential growth will be admissible. With the molecular decomposition we shall obtain an unconditional basis. As applications, we obtain the greedy basis of coorbit spaces. © 2009 Elsevier Ltd. All rights reserved.

    DOI: 10.1016/j.na.2009.03.036

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  • Wavelet bases in the weighted Besov and Triebel-Lizorkin spaces with A<inf>p</inf>loc-weights 査読

    Mitsuo Izuki, Yoshihiro Sawano

    Journal of Approximation Theory   161 ( 2 )   656 - 673   2009年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We obtain wavelet characterizations of Besov spaces and the Triebel-Lizorkin spaces associated with A∞loc-weights. These characterizations are used to show that our wavelet bases are also greedy. © 2009 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jat.2008.12.003

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  • Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces for nondoubling measures 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Mathematische Nachrichten   282 ( 12 )   1788 - 1810   2009年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WILEY-V C H VERLAG GMBH  

    We define Morrey type Besov-Triebel spaces with the underlying measure non-doubling. After defining the function spaces, we investigate boundedness property of some class of the singular integral operators. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

    DOI: 10.1002/mana.200610818

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  • Fractional integral operators in nonhomogeneous spaces 査読

    H. Gunawan, Y. Sawano, I. Sihwaningrum

    Bulletin of the Australian Mathematical Society   80 ( 2 )   324 - 334   2009年10月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:AUSTRALIAN MATHEMATICS PUBL ASSOC INC  

    We discuss here the boundedness of the fractional integral operator I a and its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness of Ia, we employ the boundedness of the so-called maximal fractional integral operator Ia,k*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type. © Australian Mathematical Publishing Association Inc. 2009.

    DOI: 10.1017/S0004972709000343

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  • A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces 査読

    Yoshihiro Sawano

    Acta Mathematica Sinica, English Series   25 ( 8 )   1223 - 1242   2009年8月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER HEIDELBERG  

    In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces. © 2009 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH.

    DOI: 10.1007/s10114-009-8247-8

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  • Truncation errors of the logarithmic potential operators 査読

    澤野嘉宏

    Proceeding of A. Razmadze Mathematical Institute   150   115 - 119   2009年

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  • A note on generalized fractional integral operators on generalized Morrey spaces 査読

    Yoshihiro Sawano, Satoko Sugano, Hitoshi Tanaka

    Boundary Value Problems   2009   2009年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:HINDAWI PUBLISHING CORPORATION  

    We show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces. Copyright © 2009 Yoshihiro Sawano et al.

    DOI: 10.1155/2009/835865

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  • Identification of the image of Morrey spaces by the fractional integral operators 査読

    澤野嘉宏, 菅野聡子, 田中仁

    Proceedings of A. Radmadze Mathematical Institute   149   87 - 93   2009年

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  • Predual spaces of morrey spaces with non-doubling measures 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Tokyo Journal of Mathematics   32 ( 2 )   471 - 486   2009年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In the present paper, we investigate the predual of the morrey spaces with non-doubling measures. we also study the modified maximal function, singular integrals and commutators on the predual spaces. © 2009 International Academic Printing Co. Ltd. All rights reserved.

    DOI: 10.3836/tjm/1264170244

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  • Generalized Morrey spaces for non-doubling measures 査読

    Yoshihiro Sawano

    Nonlinear Differential Equations and Applications   15 ( 4-5 )   413 - 425   2008年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:BIRKHAUSER VERLAG AG  

    In this paper, we define the generalized Morrey spaces on ℝ with the measure μ non-doubling. After defining the space, we shall investigate the properties of maximal operators, fractional integral operators and the singular integral operators. And we shall allude to the vector-valued extension of these operators. © 2008 Birkhäuser Verlag Basel/Switzerland.

    DOI: 10.1007/s00030-008-6032-5

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  • Quarkonial decomposition suitable for functional-differential equations of delay type 査読

    Yoshihiro Sawano, Tsuyoshi Yoneda

    Mathematische Nachrichten   281 ( 12 )   1810 - 1822   2008年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In this paper we apply quarkonial decomposition to the ordinary differential equation of delay type f′(x) = f(x -l), x ≥1. We shall derive an explicit formula in terms of the quarkonial decomposition. © 2008 WILEY-VCH Verlag, GmbH & Co. KGaA.

    DOI: 10.1002/mana.200510716

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  • Generalized Morrey spaces for non-doubling measures

    Yoshihiro Sawano

    Nonlinear Differential Equations and Applications   15 ( 4-5 )   413 - 425   2008年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In this paper, we define the generalized Morrey spaces on ℝ with the measure μ non-doubling. After defining the space, we shall investigate the properties of maximal operators, fractional integral operators and the singular integral operators. And we shall allude to the vector-valued extension of these operators. © 2008 Birkhäuser Verlag Basel/Switzerland.

    DOI: 10.1007/s00030-008-6032-5

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  • Weighted modulation space Mpqs(w) with w ∈ A∞loc 査読

    Yoshihiro Sawano

    Journal of Mathematical Analysis and Applications   345 ( 2 )   615 - 627   2008年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In the present paper, we present a natural extension of the modulation spaces Mp, qswith 0 &lt; p &lt; ∞, 0 &lt; q ≤ ∞ and s ∈ R. The weight we take up here belongs to the class A∞loc, which is even wider and contains weights of exponential growth. After defining the function spaces, we investigate their atomic and molecular decomposition as well as some elementary properties. © 2008.

    DOI: 10.1016/j.jmaa.2008.04.034

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  • Real inversion formulas of the Laplace transform on weighted function spaces 査読

    Yosihiro Sawano, Hiroshi Fujiwara, Saburou Saitoh

    Complex Analysis and Operator Theory   2 ( 3 )   511 - 521   2008年8月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:BIRKHAUSER VERLAG AG  

    We investigate compactness of linear operators associated with the real inversion formulas of the Laplace transform, coming with weighted Sobolev reproducing kernel Hilbert spaces on the half line R +. We present concrete reproducing kernels along with several typical examples. © 2008 Birkhaeuser.

    DOI: 10.1007/s11785-007-0041-y

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  • Morrey spaces with non-doubling measures II 査読

    澤野嘉宏

    Journal of the Indonesian Mathematical Society   14 ( 2 )   121 - 152   2008年

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  • Compact commutators on morrey spaces with non-doubling measures 査読

    Yoshihiro Sawano, Satoru Shirai

    Georgian Mathematical Journal   15 ( 2 )   353 - 376   2008年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:WALTER DE GRUYTER GMBH  

    We study multi-commutators on the Morrey spaces generated by BMO functions and singular integral operators or by BMO functions and fractional integral operators. We place ourselves in the setting of Rd coming with a Radon measure µ which satisfies a certain growth condition. The Morrey-boundedness of commutators is established by M. Yan and D. Yang. However, the corresponding assertion of Morrey-compactness is still missing. The aim of this paper is to prove that the multi-commutators are compact if one of the BMO functions can be approximated with compactly supported smooth functions. © 2008, Heldermann Verlag. All rights reserved.

    DOI: 10.1515/GMJ.2008.353

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  • Wavelet characterization of Besov-Morrey and Triebel-Lizorkin-Morrey spaces 査読

    Yoshihiro Sawano

    Functiones et Approximatio, Commentarii Mathematici   38 ( 1 )   93 - 107   2008年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Adam Mickiewicz University Press  

    In the present paper we characterize the Besov-Morrey spaces and the Triebel- -Lizorkin-Morrey spaces in terms of wavelet. As an application we investigate some embedding properties and diversity of the function spaces.

    DOI: 10.7169/facm/1229624654

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  • eal inversion of the Laplace transform by numerical singular value decomposition

    藤原宏志, 斎藤三郎, 松浦勉, 澤野嘉宏

    Journal of Analysis and Applications   6 ( 1 )   55--68   2008年

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  • Wavelet characterization of Besov/Triebel-Lizorkin-Morrey spaces. 査読

    澤野嘉宏

    Functiones et Approximatio   38   7 - 21   2008年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Real inversion of the Laplace transform in numerical singular value decompositions 査読

    澤野嘉宏

    Journal of Analysis and Applications   6 ( 1 )   55 - 68   2008年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Decompositions of Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Mathematische Zeitschrift   257 ( 4 )   871 - 905   2007年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER HEIDELBERG  

    The aim of this paper is to define the Besov-Morrey spaces and the Triebel- Lizorkin-Morrey spaces and to present a decomposition of functions belonging to these spaces. Our results contain an answer to the conjecture proposed by Mazzucato. © 2007 Springer-Verlag.

    DOI: 10.1007/s00209-007-0150-3

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  • Sharp maximal inequalities and commutators on morrey spaces with non-doubling measures 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Taiwanese Journal of Mathematics   11 ( 4 )   1091 - 1112   2007年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:MATHEMATICAL SOC REP CHINA  

    In this paper, we establish a sharp maximal inequality for Morrey spaces with a Radon measure μ satisfying certain growth condition, which is not necessarily doubling. As an application, we obtain the boundedness of commutators generated by singular integral or fractional integrals with RBMO functions in Morrey spaces.

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  • Atomic decomposition for the modulation space $M_{p,q}^s$ with $0<p,q \le \infty$ and $s \in {\mathbf R}$

    澤野嘉宏

    Proceedings of A.~Razmadze Mathematical Institute   145   63--68   2007年

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  • On the Young theorem for amalgams and Besov spaces 査読

    Int.~J.~Pure Appl.~Math

    澤野嘉宏,米田剛   36 ( 2 )   199 - 208   2007年

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  • The John-Nirenberg type inequality for non-doubling measures 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Studia Mathematica   181 ( 2 )   153 - 170   2007年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:POLISH ACAD SCIENCES INST MATHEMATICS  

    X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on ℝd. This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces. © Instytut Matematyczny PAN, 2007.

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  • Equivalent norms for the Morrey spaces with non-doubling measures 査読

    澤野嘉宏, 田中仁

    Far East J.~Math.~Sci.   22 ( 3 )   387--404   2006年

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  • Limiting case of the boundedness of fractional integral operators on nonhomogeneous space 査読

    Yoshihiro Sawano, Takuya Sobukawa, Hitoshi Tanaka

    Journal of Inequalities and Applications   2006 ( 7 )   1 - 16   2006年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGEROPEN  

    We show the boundedness of fractional integral operators by means of extrapolation. We also show that our result is sharp. Copyright © 2006 Yoshihiro Sawano et al.

    DOI: 10.1155/JIA/2006/92470

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  • A Vector-Valued sharp maximal inequality on morrey spaces with non-doubling measures 査読

    Yoshihiro Sawano

    Georgian Mathematical Journal   13 ( 1 )   153 - 172   2006年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    We consider the vector-valued extension of the Fefferman-Stein- Strömberg sharp maximal inequality under growth condition. As an application we obtain a vector-valued extension of the boundedness of the commutator. Furthermore, we prove the boundedness of the commutator. © 2006, Heldermann Verlag. All rights reserved.

    DOI: 10.1515/GMJ.2006.153

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  • $l^q$-valued extension of the fractional maximal operators for non-doubling measures via potential operators 査読

    澤野嘉宏

    Int.~J.~Pure Appl.~Math.   26 ( 5 )   505--523   2006年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • Morrey spaces for non-doubling measures 査読

    Yoshihiro Sawano, Hitoshi Tanaka

    Acta Mathematica Sinica, English Series   21 ( 6 )   1535 - 1544   2005年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:SPRINGER HEIDELBERG  

    The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension. © Springer-Verlag 2005.

    DOI: 10.1007/s10114-005-0660-z

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  • Sharp estimate of the modified Hardy-Littlewood maximal operator on the nonhomogeneous space via covering lemmas 査読

    澤野嘉宏

    Hokkaido Math. J.   34 ( 2 )   435--458   2005年

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  • Sharp estimates of the modified hardy littlewood maximal operator on the nonhomogeneous space via covering lemmas 査読

    Yoshihiro Sawano

    Hokkaido Mathematical Journal   34 ( 2 )   435 - 458   2005年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    In this paper we consider the modified maximal operator on the separable metric space. Define [Formula] and [Formula] respectively. We investigate in what parameter k the weak (1, 1)-inequality holds for Mk and Mk, uc in general metric space and Euclidean space. The proofs are sharper than the method of Vitali’s covering lemma. This attempt is partially done by Yutaka Terasawa [9] before. When we investigate Rd, we prove a new covering lemma of Rd. We also show that our condition on parameter k is sharp. In connection with this we consider the dual inequality of Stein type and its applications. © 2005 by the University of Notre Dame. All rights reserved.

    DOI: 10.14492/hokmj/1285766231

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書籍等出版物

  • Morrey spaces : introduction and applications to integral operators and PDE's

    澤野, 嘉宏, Di Fazio, Giuseppe, Hakim, Denny Ivanal

    C&H/CRC Press  2020年  ( ISBN:9781498765510

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    総ページ数:xxi, 479 p.   記述言語:英語  

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  • Theory of Besov Spaces

    澤野嘉宏( 担当: 単著)

    スプリンガー  2018年11月 

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  • ベゾフ空間論

    澤野嘉宏( 担当: 単著)

    日本評論社  2018年  ( ISBN:9789811308352

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    総ページ数:xxiii, 945 p.   記述言語:英語  

    ASIN

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  • 再生核の応用についての総合的な研究

    齋藤 三郎, 澤野 嘉宏, 京都大学数理解析研究所

    京都大学数理解析研究所  2016年1月 

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    総ページ数:ii, 239p  

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  • Theory of reproducing kernels and applications

    齋藤, 三郎, 澤野, 嘉宏

    Springer  2016年  ( ISBN:9789811005299

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    総ページ数:xviii, 452 p.   記述言語:英語  

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  • 早わかりルベーグ積分 (数学のかんどころ 29)

    澤野 嘉宏( 担当: 単著)

    共立出版  2015年9月  ( ISBN:4320110706

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    総ページ数:203  

    ASIN

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  • 早わかりルベーグ積分

    澤野, 嘉宏

    共立出版  2015年9月  ( ISBN:9784320110700

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    総ページ数:viii, 203p   記述言語:日本語  

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  • 早わかりベクトル解析 ―3つの定理が織りなす華麗な世界― (数学のかんどころ 25)

    澤野 嘉宏, 飯高 茂, 中村 滋, 岡部 恒治, 桑田 孝泰( 担当: 単著)

    共立出版  2014年5月  ( ISBN:4320110668

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    総ページ数:195  

    ASIN

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  • 早わかりベクトル解析 : 3つの定理が織りなす華麗な世界

    澤野, 嘉宏

    共立出版  2014年5月  ( ISBN:9784320110663

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    総ページ数:ix, 195p   記述言語:日本語  

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  • ベゾフ空間論 = Theory of Besov spaces

    澤野, 嘉宏

    日本評論社  2011年1月  ( ISBN:9784535786455

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    総ページ数:xii, 426p   記述言語:日本語  

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  • Morrey spaces for non-doubling measures = Doubling条件を満たしていない測度に対するMorrey空間

    澤野 嘉宏

    東京大学数理科学研究科  2006年 

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    総ページ数:1冊   記述言語:英語  

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MISC

  • 現代数学の眺め 調和解析

    澤野嘉宏

    数理科学   59 ( 6 )   45 - 51   2021年

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    記述言語:日本語   出版者・発行元:サイエンス社  

    CiNii Books

    J-GLOBAL

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  • Complex interpolation of vanishing Morrey spaces 査読

    Denny Ivanal Hakim, Yoshihiro Sawano

    Annals of Functional Analysis   11 ( 3 )   643 - 661   2020年7月

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    出版者・発行元:Springer Science and Business Media LLC  

    We describe the first and second complex interpolations of vanishing Morrey spaces, introduced in Almeida and Samko (J Funct Anal 2726:2392–2411, 2017) and Chiarenza and Franciosi (Ann Mat Pura Appl 161(4):285–297, 1992). In addition, we show that the diamond subspace in Hakim et al. (Constr Approx 46:489–563, 2017) and one of the function spaces in [1] are the same. We also give several examples for showing that each of the complex interpolations of these spaces is different.

    DOI: 10.1007/s43034-019-00045-w

    Scopus

    arXiv

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    その他リンク: http://arxiv.org/pdf/1906.03941v1

  • A NOTE ON THE BILINEAR FRACTIONAL INTEGRAL OPERATOR ACTING ON MORREY SPACES 査読

    Naoya Hatano, Yoshihiro Sawano

    173 ( 3 )   37 - 44   2019年12月

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    担当区分:筆頭著者, 責任著者  

    Scopus

    arXiv

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    その他リンク: http://arxiv.org/pdf/1904.00574v1

  • 滑らかさを加味した直交ストリッカーツ評価 (関数空間の一般化とその周辺)

    BEZ NEAL, HONG YOUNGHUN, LEE SANGHYUK, 中村 昌平, 澤野 嘉宏

    数理解析研究所講究録 = RIMS Kokyuroku   ( 2143 )   173 - 184   2019年12月

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    記述言語:日本語   出版者・発行元:京都大学数理解析研究所  

    直交ストリッカーツ評価と呼ばれる新しい評価を示す. 最初に, FrankとSabinによる関数の滑らかさを加味しない直交ストリッカーツ評価[5]を示し, 後で我々による関数の滑らかさを加味した直交ストリッカーツ評価のひとつの場合の証明する. この結果は我々の論文[2]として出版されている.

    CiNii Books

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  • Composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions

    Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    511 ( 1 )   2019年11月

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    Composition operators have been extensively studied in complex analysis, and<br />
    recently, they have been utilized in engineering and machine learning. Here, we<br />
    focus on composition operators associated with maps in Euclidean spaces that<br />
    are on reproducing kernel Hilbert spaces with respect to analytic positive<br />
    definite functions, and prove the maps are affine if the composition operators<br />
    are bounded. Our result covers composition operators on Paley-Wiener spaces and<br />
    reproducing kernel spaces with respect to the Gaussian kernel on ${\mathbb<br />
    R}^d$, widely used in the context of engineering.

    DOI: 10.1016/j.jmaa.2022.126048

    Scopus

    arXiv

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  • Conditions for boundedness into Hardy spaces 査読

    Loukas Grafakos, Shohei Nakamura, Hanh Van Nguyen, Yoshihiro Sawano

    Mathematische Nachrichten   292 ( 11 )   2383 - 2410   2019年11月

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    担当区分:責任著者  

    We obtain the boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman–Meyer class, sums of products of linear Calderón–Zygmund operators and combinations of these two types.

    DOI: 10.1002/mana.201800252

    Scopus

    arXiv

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    その他リンク: http://arxiv.org/pdf/1702.02229v1

  • Paraproduct in Besov–Morrey spaces 招待 査読

    Yoshihiro Sawano

    Springer Proceedings in Mathematics and Statistics   291   117 - 133   2019年

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    担当区分:筆頭著者, 責任著者  

    The paraproduct plays a key role in some highly singular partial differential equations. For example, that for Hölder–Zygmund spaces is used to solve stochastic differential equations, as demonstrated by Gubinelli, Imkeller, Perkowski, and Hairer. In this note, which is organized in a self-contained manner, the counterparts for Besov Morrey spaces are obtained.

    DOI: 10.1007/978-3-030-26748-3_8

    Scopus

    arXiv

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    その他リンク: http://arxiv.org/pdf/1812.08379v1

  • 一般のパラメータに対するモレー空間の複素補間について (関数空間の深化とその周辺)

    澤野 嘉宏

    数理解析研究所講究録   ( 2095 )   15 - 22   2018年12月

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    記述言語:日本語   出版者・発行元:京都大学数理解析研究所  

    本研究は関数空間の補間についてである. 特にモレー空間を調べる. 第二補間空間の見える化をすることが目的である. この研究はDenny Ivanal Hakim氏, Miestyslaw Mastylo氏, 中村昌平氏, 曽布川拓也氏との共同研究である. とくに, 現時点では投稿中のMicstyslaw Mastylo氏との研究成果について説明する.

    CiNii Books

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    その他リンク: http://hdl.handle.net/2433/251699

  • Paracontrolled quasi-geostrophic equation with space-time white noise

    Yuzuru Inahama, Yoshihiro Sawano

    2018年6月

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    記述言語:英語   掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    We study the stochastic dissipative quasi-geostrophic equation with
    space-time white noise on the two-dimensional torus. This equation is highly
    singular and basically ill-posed in its original form. The main objective of
    the present paper is to formulate and solve this equation locally in time in
    the framework of paracontrolled calculus when the differential order of the
    main term, the fractional Laplacian, is larger than $7/4$. No renormalization
    has to be done for this model.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1806.00564v3

  • The global optimum of shallow neural network is attained by ridgelet transform

    Sho Sonoda, Isao Ishikawa, Masahiro Ikeda, Kei Hagihara, Yoshihiro Sawano, Takuo Matsubara, Noboru Murata

    2018年5月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    We prove that the global minimum of the backpropagation (BP) training problem<br />
    of neural networks with an arbitrary nonlinear activation is given by the<br />
    ridgelet transform. A series of computational experiments show that there<br />
    exists an interesting similarity between the scatter plot of hidden parameters<br />
    in a shallow neural network after the BP training and the spectrum of the<br />
    ridgelet transform. By introducing a continuous model of neural networks, we<br />
    reduce the training problem to a convex optimization in an infinite dimensional<br />
    Hilbert space, and obtain the explicit expression of the global optimizer via<br />
    the ridgelet transform.

    arXiv

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  • Preface

    Yoshihiro Sawano

    Developments in Mathematics   56   vii - x   2018年

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  • 書評 数学解析第一編 微分積分学 第1巻 改訂新編 藤原松三郎著,浦川肇,髙木泉,藤原毅夫編著

    澤野 嘉宏

    数学通信   22 ( 3 )   79 - 81   2017年11月

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    記述言語:日本語   出版者・発行元:日本数学会  

    CiNii Books

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  • Generalized Hardy spaces based on Banach function spaces (関数空間の構造とその周辺)

    Sawano Yoshihiro

    数理解析研究所講究録   ( 2041 )   1 - 10   2017年7月

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    記述言語:英語   出版者・発行元:京都大学数理解析研究所  

    CiNii Books

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  • Multiplier conditions for Boundedness into Hardy spaces

    Loukas Grafakos, Shohei Nakamura, Hanh Van Nguyen, Yoshihiro Sawano

    2017年2月

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    In the present work, we find useful and explicit necessary and sufficient
    conditions for linear and multilinear multiplier operators of Coifman-Meyer
    type, finite sum of products of Calder\'on-Zygmund operators, and also of
    intermediate types to be bounded from a product of Lebesgue or Hardy spaces
    into a Hardy space. These conditions state that the symbols of the multipliers
    $\sigma(\xi_1,\dots , \xi_m)$ and their derivatives vanish on the hyperplane
    $\xi_1+\cdots+\xi_m=0$.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1702.08190v1

  • Fundamental properties of RKHS

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   65 - 160   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    In Chap. 2, which is at the heart of this book, we develop the general theory of reproducing kernels and its fundamental properties. First, we establish that any positive definite kernel corresponds uniquely to an RKHS. Then we discuss operations for RKHS. These operations will be fundamental for applications. After clarifying the basic properties, we will present the methods to construct RKHSs. One of the ideas is to use complete orthonormal systems or the Fourier integral. Finally, we discuss the relation between RKHS and linear mappings. One of the powerful properties that RKHSs enjoy is that we can characterize completely the image of linear mappings. But the proof of the results presented earlier than Sect. 2.4 is independent from Sect. 2.4. We list [209, 347, 403] for the introduction of theory of reproducing kernel Hilbert spaces.

    DOI: 10.1007/978-981-10-0530-5_2

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  • Applications to partial differential equations

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   231 - 294   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    In this chapter, we gather concrete results on typical linear partial differential equations using Tikhonov regularization and a finite number of data.

    DOI: 10.1007/978-981-10-0530-5_6

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  • Definitions and examples of reproducing Kernel Hilbert spaces

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   1 - 63   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    In Chap. 1 we introduce many examples of reproducing kernel Hilbert spaces (RKHSs for short). The reader may skip Chap. 1 and later go back to it if needed. We will consider RKHSs of Sobolev type, of Paley Wiener type, on the complex plane C, and of polynomial and graph types. We will use the examples for later considerations.

    DOI: 10.1007/978-981-10-0530-5_1

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  • Real inversion formulas of the Laplace transform

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   197 - 215   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    As stated in the preface, one of our strong motivations for writing this book is given by the historical success of the numerical and real inversion formulas of the Laplace transform which is a famous typical ill-posed and very difficult problem. In this chapter, we will see their mathematical theory and formulas, as a clear evidence of the definite power of the theory of reproducing kernels when combined with the Tikhonov regularization.

    DOI: 10.1007/978-981-10-0530-5_4

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  • Moore Penrose generalized inverses and tikhonov regularization

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   161 - 196   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    By applying the general theory of reproducing kernels, we will consider the practical constructions of approximate solutions for bounded linear operator equations.

    DOI: 10.1007/978-981-10-0530-5_3

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  • Applications to ordinary differential equations

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   217 - 230   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    We will give concrete representation formulas of the approximate solutions for linear ordinary differential equations following the Tikhonov regularization and using a finite number of data. For other applications of reproducing kernels, see a series of papers; for example, [128, 177-181, 232, 233, 283, 284]. In these papers reproducing kernels are applied to nonlinear differential equations using many concrete reproducing kernels with numerical experiments given as well. See also the recent article [477].

    DOI: 10.1007/978-981-10-0530-5_5

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  • Special topics on reproducing kernels

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   321 - 386   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    In this chapter, we will gather simply several special hot and important topics from the viewpoint of the general theory of reproducing kernels.

    DOI: 10.1007/978-981-10-0530-5_8

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  • Applications to integral equations

    Saburou Saitoh, Yoshihiro Sawano

    Developments in Mathematics   44   205 - 319   2016年10月

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    記述言語:英語   出版者・発行元:Springer New York LLC  

    Singular integral equations are presently encountered in a wide range of mathematical models, for instance in acoustics, fluid dynamics, elasticity and fracture mechanics. Together with these models, a variety of methods and applications for these integral equations has been developed. For fracture mechanics and crack, see [101, 102, 144] for example. Singular integral equations are derived from physical equations using the Fourier transform, the Plemeli formula, and distribution theory.

    DOI: 10.1007/978-3-319-42023-3_5

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  • Certain identities on derivatives of radial homogeneous and logarithmic functions

    Kei Morii, Tokushi Sato, Yoshihiro Sawano

    2016年6月

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    Let $k$ be a natural number and $s$ be real. In the 1-dimensional case, the
    $k$-th order derivatives of the functions $\lvert x\rvert^s$ and $\log \lvert
    x\rvert$ are multiples of $\lvert x\rvert^{s-k}$ and $\lvert x\rvert^{-k}$,
    respectively. In the present paper, we generalize this fact to higher
    dimensions by introducing a suitable norm of the derivatives, and give the
    exact values of the multiples.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1606.06155v1

  • Equivalent norms for the Morrey spaces with non-doubling measures

    Hitoshi Tanaka, Yoshihiro Sawano

    2016年6月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    In this paper under some growth condition we investigate the connection
    between RBMO and the Morrey spaces. We do not assume the doubling condition
    which has been a key property of harmonic analysis. We also obtain another type
    of equivalent norms.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1606.02787v1

  • A note on the boundedness of discrete commutators on Morrey spaces and their preduals

    Yoshihiro Sawano

    2016年6月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    Dyadic fractional integral operators are shown to be bounded on Morrey spaces
    and their preduals. It seems that the proof of the boundedness by means of
    dyadic fractional integral operators is effective particularly on the preduals.
    In the present paper the commutators are proved to be bounded as well.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1606.02791v1

  • The singular integral operator and its commutator on weighted Morrey spaces

    Shohei Nakamura, Yoshihiro Sawano

    2016年6月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    In this paper, we give necessary conditions and sufficient conditions
    respectively for the boundedness of the singular integral operator on the
    weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey
    spaces; the $A_q$-theory by Muckenhoupt and Wheeden does not suffice. We also
    discuss the boundedness of the commutators. The difference between the maximal
    operator and the singular integral operators will be clarified. Further, the
    property of the sharp maximal operator is investigated.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1606.00971v2

  • An observation of the subspaces of ${\mathcal S}'$ 招待 査読

    Yoshihiro Sawano

    2016年3月

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    記述言語:英語   掲載種別:記事・総説・解説・論説等(国際会議プロシーディングズ)  

    The spaces ${\mathcal S}'/{\mathcal P}$ equipped with the quotient topology
    and ${\mathcal S}'_\infty$ equipped with the weak-* topology are known to be
    homeomorphic, where ${\mathcal P}$ denotes the set of all polynomials. The
    proof is a combination of the fact in the textbook by Treves and the well-known
    bipolar theorem. In this paper by extending slightly the idea employed in
    \cite{NNS15}, we give an alternative proof of this fact and then we extend this
    proposition so that we can include some related function spaces.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1603.07890v2

  • Homogeneous Besov spaces

    Yoshihiro Sawano

    2016年3月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    This note is based on a series of lectures delivered in Kyoto University.<br />
    This note surveys the homogeneous Besov space $\dot{B}^s_{pq}$ on ${\mathbb<br />
    R}^n$ with $1 \le p,q \le \infty$ and $s \in {\mathbb R}$ in a rather<br />
    self-contained manner. Possible extensions of this type of function spaces are<br />
    breifly discussed in the end of this article. In particular, the fundamental<br />
    properties are stated for the spaces $\dot{B}^s_{pq}$ with $0&lt;p,q \le \infty$<br />
    and $s \in {\mathbb R}$ and $\dot{F}^s_{pq}$ with $0&lt;p&lt;\infty$, $0&lt;q \le<br />
    \infty$ and $s \in {\mathbb R}$ as well as nonhomogeneous coupterparts<br />
    $B^s_{pq}$ with $0&lt;p,q \le \infty$ and $s \in {\mathbb R}$ and $F^s_{pq}$ with<br />
    $0&lt;p&lt;\infty$, $0&lt;q \le \infty$ and $s \in {\mathbb R}$.

    arXiv

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  • Pasting reproducing kernel Hilbert spaces (再生核の応用についての総合的な研究 : RIMS研究集会報告集)

    Sawano Yoshihiro

    数理解析研究所講究録   1980 ( 1980 )   103 - 105   2016年1月

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    記述言語:英語   出版者・発行元:京都大学数理解析研究所  

    CiNii Books

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    その他リンク: http://hdl.handle.net/2433/224447

  • What are reproducing kernels? (再生核の応用についての総合的な研究 : RIMS研究集会報告集)

    Saitoh Saburou, Sawano Yoshihiro

    数理解析研究所講究録   1980 ( 1980 )   200 - 206   2016年1月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学数理解析研究所  

    CiNii Books

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    その他リンク: http://hdl.handle.net/2433/224439

  • An introduction of the book "Theory of Reproducing Kernels and Applications" (再生核の応用についての総合的な研究 : RIMS研究集会報告集)

    Sawano Yoshihiro, Saitoh Saburou

    数理解析研究所講究録   1980 ( 1980 )   95 - 102   2016年1月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学数理解析研究所  

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    その他リンク: http://hdl.handle.net/2433/224448

  • General initial value problems using eigenfunctions and reproducing kernels (preliminaries report) (再生核の応用についての総合的な研究 : RIMS研究集会報告集)

    Saitoh Saburou, Sawano Yoshihiro

    数理解析研究所講究録   1980 ( 1980 )   106 - 124   2016年1月

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    記述言語:英語   出版者・発行元:京都大学数理解析研究所  

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    その他リンク: http://hdl.handle.net/2433/224446

  • エレガントな解答をもとむ 解答 : 出題 2014年12月号 招待

    澤野 嘉宏, 秋山 仁

    数学セミナー   54 ( 3 )   92 - 98   2015年3月

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    記述言語:日本語   出版者・発行元:日本評論社  

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  • Fractional type Marcinkiewicz integral operators associated to surfaces

    Yoshihiro Sawano, Kozo Yabuta

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2014年6月

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    記述言語:英語   掲載種別:機関テクニカルレポート,技術報告書,プレプリント等   出版者・発行元:SPRINGER INTERNATIONAL PUBLISHING AG  

    In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and we extend a result given by Chen et al. (J. Math. Anal. Appl. 276:691-708, 2002). They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel-Lizorkin spaces (F)over dot(pq)(alpha)(R-n) to L-p(R-n). Recently the second author, together with Xue and Yan, greatly weakened their assumptions. In this paper, we extend their results to the case where the operators are associated to the surfaces of the form {x = phi(vertical bar y vertical bar)y/vertical bar y vertical bar} subset of R-n x (R-n \ {0}). To prove our result, we discuss a characterization of the homogeneous Triebel-Lizorkin spaces in terms of lacunary sequences.

    DOI: 10.1186/1029-242X-2014-232

    Web of Science

    arXiv

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  • 知っておくべき解析学のことば (特集 知っておくべき数学のことば) 招待

    澤野 嘉宏

    数学セミナー   53 ( 5 )   22 - 27   2014年5月

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    記述言語:日本語   出版者・発行元:日本評論社  

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  • The Fatou property of block spaces

    Yoshihiro Sawano, Hitoshi Tanaka

    2014年4月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    Around thirty years ago, block spaces, which are the predual of Morrey
    spaces, had been considered. However, it seems that there is no proof that
    block spaces satisfy the Fatou property. In this paper the Fatou property for
    block spaces is verified and the predual of block spaces is characterized.

    arXiv

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    その他リンク: http://arxiv.org/pdf/1404.2688v1

  • A bilinear estimate for commutators of fractional integral operators (Potential Theory and its Related Fields)

    SAWANO Yoshihiro, SUGANO Satoko, TANAKA Hitoshi

    数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu   43   155 - 170   2013年9月

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    記述言語:英語   出版者・発行元:京都大学  

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  • Olsen's inequality and its applications to the MHD equations (Regularity and Singularity for Geometric Partial Differential Equations and Conservation Laws)

    澤野 嘉宏, 田中 仁, 菅野 聡子, Gala Sadek

    数理解析研究所講究録   1845 ( 1845 )   121 - 144   2013年7月

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    記述言語:日本語   出版者・発行元:京都大学数理解析研究所  

    CiNii Books

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    その他リンク: http://hdl.handle.net/2433/195037

  • 分数べき積分作用素の離散化に関して (時間周波数解析の理論とその理工学的応用 : RIMS共同研究報告集)

    澤野 嘉宏

    数理解析研究所講究録   1803 ( 1803 )   1 - 11   2012年8月

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    記述言語:日本語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学  

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  • 分数べき積分作用素の離散化に関して (時間周波数解析の理論とその理工学的応用)

    澤野 嘉宏

    数理解析研究所講究録   1803 ( 1803 )   1 - 11   2012年8月

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    記述言語:日本語   出版者・発行元:京都大学数理解析研究所  

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  • Olsen's inequality and its applications to Schrodinger equations (Harmonic Analysis and Nonlinear Partial Differential Equations)

    SAWANO Yoshihiro, SUGANO Satoko, TANAKA Hitoshi

    RIMS Kokyuroku Bessatsu   26   51 - 80   2011年5月

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    記述言語:英語   出版者・発行元:京都大学  

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  • Loukas Grafakos: Classical Fourier Analysis, 2nd Ed. & Modern Fourier Analysis, 2nd Ed., Springer, Grad. Texts in Math., 249 & 250, 2008年, xvi + 489ページ & 2009年, xv + 504ページ.

    澤野 嘉宏

    数学   63 ( 2 )   249 - 253   2011年

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    記述言語:日本語   出版者・発行元:一般社団法人 日本数学会  

    DOI: 10.11429/sugaku.0632249

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  • 書評 Loukas Grafakos: Classical Fourier analysis, 2nd ed. & Modern Fourier analysis, 2nd ed. 招待 査読

    澤野 嘉宏

    数学   63 ( 2 )   249 - 253   2011年

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    記述言語:日本語   掲載種別:書評論文,書評,文献紹介等   出版者・発行元:日本数学会  

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  • Weighted Besov-Morrey spaces and Triebel-Lizorkin spaces (Harmonic Analysis and Nonlinear Partial Differential Equations) 招待 査読

    出来 光夫, 澤野 嘉宏, 田中 仁

    数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu   22 ( 22 )   21 - 60   2010年12月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(国際会議)   出版者・発行元:京都大学数理解析研究所  

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  • エレガントな解答をもとむ 解答--出題 2010年8月号

    澤野 嘉宏, 和田出 秀光, 上原 隆平

    数学セミナー   49 ( 11 )   94 - 101   2010年11月

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    記述言語:日本語   出版者・発行元:日本評論社  

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  • Discretization by the theory of reproducing kernels (数値解析と数値計算アルゴリズムの最近の展開--RIMS研究集会報告集)

    Castro Luis P., 齋藤 三郎, 澤野 嘉宏, Simoes Alberto M.

    数理解析研究所講究録   1719 ( 1719 )   142 - 154   2010年11月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学数理解析研究所  

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    その他リンク: http://hdl.handle.net/2433/170354

  • 面積,体積とは何か--ジョルダン測度とルベーグ測度 (特集 「実解析」とは何か)

    澤野 嘉宏

    数学セミナー   49 ( 10 )   13 - 18   2010年10月

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    記述言語:日本語   出版者・発行元:日本評論社  

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  • 線形常微分方程式のチコノフの正則化による近似解法について

    CASTRO Luis, 斎藤三郎, 澤野嘉宏, SILVA Anabela

    理論応用力学講演会講演論文集   59th ( 0 )   185 - 185   2010年

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    記述言語:日本語   掲載種別:会議報告等   出版者・発行元:日本学術会議 「機械工学委員会・土木工学・建築学委員会合同IUTAM分科会」  

    この講演ではチコノフの正則化法を用いて微分方程式の近似解の構成方法を提示する。近似の位相は一様収束を想定している。簡単な例を用いて数値例も構成する。離散のデーターからいかにして近似解を与えるかに焦点を当てる。

    DOI: 10.11345/japannctam.59.0.185.0

    J-GLOBAL

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  • エレガントな解答をもとむ 解答--出題 2009年7月号 招待

    澤野 嘉宏, 矢ヶ部 巖

    数学セミナー   48 ( 10 )   100 - 107   2009年10月

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    記述言語:日本語   出版者・発行元:日本評論社  

    CiNii Books

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  • Holderの不等式 (特集 不等式の世界) 招待

    澤野 嘉宏

    数学セミナー   48 ( 2 )   17 - 21   2009年2月

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    記述言語:日本語   出版者・発行元:日本評論社  

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  • Numerical Real Inversion of the Laplace Transform by using a high-acuuracy numerical method 査読

    H. Fujiwara, T. Matsuura, S. Saitoh, Y. Sawano

    Further Progress in Analysis, World Scientific   574 - 585   2009年

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  • ラプラス変換の実逆変換への再生核空間の応用(2) (再生核の応用についての研究--RIMS研究集会報告集)

    梶野 直孝, 澤野 嘉宏, 藤原 宏志

    数理解析研究所講究録   1618 ( 1618 )   189 - 191   2008年12月

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    記述言語:英語   出版者・発行元:京都大学数理解析研究所  

    CiNii Books

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    その他リンク: http://hdl.handle.net/2433/140182

  • ラプラス変換の実逆変換への再生核空間の応用 (再生核の応用についての研究)

    澤野 嘉宏, 藤原 宏志, 齋藤 三郎

    数理解析研究所講究録   1618   175 - 188   2008年12月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学  

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  • Maximal operator for pseudo-differential operators with homogeneous symbols

    Yoshihiro Sawano

    2008年9月

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    掲載種別:機関テクニカルレポート,技術報告書,プレプリント等  

    The aim of the present paper is to obtain a Sj\"{o}lin-type maximal estimate
    for pseudo-differential operators with homogeneous symbols. The crux of the
    proof is to obtain a phase decomposition formula which does not involve the
    time traslation. The proof is somehow parallel to the paper by Pramanik and
    Terwilleger (P. Malabika and E. Terwilleger, A weak $L^2$ estimate for a
    maximal dyadic sum operator on $R^n$, Illinois J. Math, {\bf 47} (2003), no. 3,
    775--813). In the present paper, we mainly concentrate on our new phase
    decomposition formula and the results in the Cotlar type estimate, which are
    different from the ones by Pramanik and Terwilleger.

    arXiv

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    その他リンク: http://arxiv.org/pdf/0809.2313v1

  • Functional differential equations of a type similar to f´(x)=2f(2x+1)-2f(2x-1) and its application to Poisson's equation (調和解析学と非線形偏微分方程式--RIMS研究集会報告集)

    澤野 嘉宏, 米田 剛

    数理解析研究所講究録   1529   97 - 109   2007年1月

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    記述言語:英語   出版者・発行元:京都大学  

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  • doubling 条件を満たさない測度空間上のMorrey 空間に関して(調和解析と非線形偏微分方程式)

    澤野 嘉宏, 田中 仁

    数理解析研究所講究録   1491   106 - 125   2006年5月

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    記述言語:英語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学  

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  • ある関数とクオーク分解に関して(関数方程式の解のダイナミクスと数値シミュレーション)

    澤野 嘉宏, 米田 剛

    数理解析研究所講究録   1474   60 - 66   2006年2月

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    記述言語:日本語   掲載種別:研究発表ペーパー・要旨(全国大会,その他学術会議)   出版者・発行元:京都大学  

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▼全件表示

講演・口頭発表等

  • The John-Nirenberg type inequality for non-doubling measures

    澤野嘉宏, 田中仁

    Proceedings of the Harmonic Analysis and its Application at Sapporo 

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  • Inclusions in Generalized Orlicz Spaces

    Yoshihiro Sawano, Seyyed Mohammad Tabatabaie

    Bulletin of the Iranian Mathematical Society  2021年8月  SPRINGER SINGAPORE PTE LTD

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    開催年月日: 2021年8月    

    記述言語:英語  

    In this paper, we give some equivalent conditions to have an inclusion between two generalized Orlicz spaces. One of these conditions does not depend on generalized Young functions. The obtained results improve the famous ones on Lebesgue spaces.

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  • Disjoint dynamics of weighted translations on solid spaces

    Yoshihiro Sawano, Seyyed Mohammad Tabatabaie, Fatemeh Shahhoseini

    Topology and its Applications  2021年7月  ELSEVIER

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    開催年月日: 2021年7月    

    記述言語:英語  

    In this paper, applying the new concept of aperiodic functions, we characterize disjoint hypercyclic and disjoint topologically mixing weighted translation operators on general Banach lattices. The obtained results in addition to previous modes of Lebesgue and Orlicz spaces, also cover new classes such as some closed subspaces of Morrey spaces.

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  • Complex interpolation of the predual of Morrey spaces over measure spaces

    Victor I. Burenkov, Denny I. Hakim, Eiichi Nakai, Yoshihiro Sawano, Takuya Sobukawa, Tamara V. Tararykova

    Georgian Mathematical Journal  2021年6月 

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    開催年月日: 2021年6月    

    We prove that block spaces defined on ℝn with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product.

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  • Weighted Hankel Transform and Its Applications to Fourier Transform

    Masami Okada, Yoshihiro Sawano

    Journal of Fourier Analysis and Applications  2021年4月 

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    開催年月日: 2021年4月    

    The purpose of the present paper is to discuss the integrability of the Fourier transform of L∞-functions subject to a very weak decay condition. This will include the negative power of the logarithm. For a start, the case when d= 1 is investigated by the use of the second mean value theorem. Based on the discussion of this case, a passage to the weighted Hankel transform is done, which covers the integrability of the d-dimensional Fourier transform of the radial functions.

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  • Complex Interpolation and the Adams Theorem

    Yoshihiro Sawano, Satoko Sugano

    Potential Analysis  2021年2月  Springer Science and Business Media {LLC}

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    開催年月日: 2021年2月    

    記述言語:英語  

    Recently, many researchers investigated the description of the complex interpolation of Morrey spaces. Among others, the second complex interpolation of Morrey spaces turned out to be the Calderón product of Morrey spaces. In this paper as an application of this fact, we propose an improvement of the Adams theorem asserting that the fractional integral operator maps Morrey spaces to other Morrey spaces.

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  • Generalized fractional integral operators on Orlicz–Hardy spaces

    Ryutaro Arai, Eiichi Nakai, Yoshihiro Sawano

    Mathematische Nachrichten  2021年2月  Wiley

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    開催年月日: 2021年2月    

    The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space (Formula presented.) to another Orlicz–Hardy space (Formula presented.), where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator (Formula presented.) from (Formula presented.) to (Formula presented.) for (Formula presented.) and (Formula presented.), which was proved by Stein and Weiss in 1960.

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  • The spectra of the generalized difference operators on the spaces of convergent series

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Linear and Multilinear Algebra  2021年  Informa {UK} Limited

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    開催年月日: 2021年    

    An investigation is made on the spectrum and fine spectrum of the generalized difference operator (Formula presented.) on the space (Formula presented.) of convergent series. Some related results, concerning the spectrum of the adjoint operator (Formula presented.) on the space (Formula presented.) of bounded variation sequences, are also derived. Further, some special cases of the main results are investigated deeper.

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  • Boundedness of composition operators on Morrey spaces and weak Morrey spaces

    Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

    Journal of Inequalities and Applications  2021年 

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    開催年月日: 2021年    

    In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As this specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.

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  • Local Muckenhoupt class for variable exponents

    Toru Nogayama, Yoshihiro Sawano

    Journal of Inequalities and Applications  2021年 

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    開催年月日: 2021年    

    This work extends the theory of Rychkov, who developed the theory of Aploc weights. It also extends the work by Cruz-Uribe SFO, Fiorenza, and Neugebauer. The class Ap(⋅)loc is defined. The weighted inequality for the local Hardy–Littlewood maximal operator on Lebesgue spaces with variable exponents is proven. Cruz-Uribe SFO, Fiorenza, and Neugebauer considered the Muckenhoupt class for Lebesgue spaces with variable exponents. However, due to the setting of variable exponents, a new method for extending weights is needed. The proposed extension method differs from that by Rychkov. A passage to the vector-valued inequality is realized by means of the extrapolation technique. This technique is an adaptation of the work by Cruz-Uribe and Wang. Additionally, a theory of extrapolation adapted to our class of weights is also obtained.

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  • Some modular inequalities in lebesgue spaces with a variable exponent

    Mitsuo Izuki, Takahiro Noi, Yoshihiro Sawano

    Transactions of A. Razmadze Mathematical Institute  2020年12月 

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    開催年月日: 2020年12月    

    Our aim is to study the modular inequalities for some operators, for example, the Bergman projection in Lebesgue spaces with a variable exponent. Under proper assumptions on the variable exponent, we prove that the modular inequalities hold, if and only if the exponent almost everywhere is equal to a constant. In order to get the main results, we establish a lower pointwise bound for these operators of a characteristic function.

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  • Sparse non-smooth atomic decomposition of Morrey spaces

    Yoshihro Sawano

    Mathematical Methods in the Applied Sciences  2020年11月  Wiley

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    開催年月日: 2020年11月    

    記述言語:英語  

    Recently, a non-smooth atomic decomposition in Morrey spaces was obtained by the author, Iida and Tanaka. This note refines the above existing result using the notion of sparse families. As an application, we prove the equivalence between fractional integral operators and fractional maximal operators under the Morrey norm.

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  • Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent

    Mitsuo Izuki, Toru Nogayama, Takahiro Noi, Yoshihiro Sawano

    Nonlinear Analysis, Theory, Methods and Applications  2020年9月  Elsevier {BV}

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    開催年月日: 2020年9月    

    Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular inequalities to hold. One big achievement is that the weights with exponential growth can be handled in the framework of variable exponents.

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    その他リンク: http://arxiv.org/pdf/1912.03400v1

  • Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces

    Yoshihiro Sawano, Tetsu Shimomura

    Georgian Mathematical Journal  2020年9月  WALTER DE GRUYTER GMBH

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    開催年月日: 2020年9月    

    記述言語:英語  

    The predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

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  • Bilinear rough singular integral operators on Morrey spaces

    Daniel Salim, Yoshihiro Sawano, Pebrudal Zanu

    Journal of Analysis  2020年9月 

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    開催年月日: 2020年9月    

    Recently Grafakos et al., have proved that the bilinear rough singular integral operators are bounded on Lebesgue spaces. Here we aim to show that these operators extend to bounded linear operators on Morrey spaces as well. Although the proof hinges on the boundedness due to Grafakos et al., the proof seems to give a general technique to prove or extend the boundedness of the operators.

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  • Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces

    Yoshihiro Sawano, Saad R. El-Shabrawy

    Monatshefte fur Mathematik  2020年5月  SPRINGER WIEN

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    開催年月日: 2020年5月    

    記述言語:英語  

    This paper concerns the spectrum and the fine spectrum of the discrete generalized Cesàro operator Ct, where 0 ≤ t< 1 , on Banach sequence spaces close to ℓ1 and ℓ∞. We derive some compactness results for the operator Ct to describe the spectrum. Our technique involves standard operator theory and summability theory.

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  • Complex interpolation of various subspaces of Morrey spaces

    Denny Ivanal Hakim, Yoshihiro Sawano

    Science China Mathematics  2020年5月 

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    開催年月日: 2020年5月    

    In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces. We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al. (2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano (2017) and Hakim et al. (2017).

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  • Homogeneous Besov spaces

    Yoshihiro Sawano

    Kyoto Journal of Mathematics  2020年4月  DUKE UNIV PRESS

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    開催年月日: 2020年4月    

    記述言語:英語  

    This note is based on a series of lectures delivered at Kyoto University in 2015. This note surveys the homogeneous Besov space Bspq on ℝn with 1 < p, q < ∞ and s ∈ ℝ in a rather self-contained manner. Among other results, we show that S′∞ and S′/P are isomorphic, and we also discuss the realizations in Bspq. The fact that S′∞ and S′/P are isomorphic can be found in textbooks. The realization of Bspq can be found in works by Bahouri, Chemin, and Danchin and by Bourdaud for example. Here, we prove these facts using fundamental results in functional analysis such as the Hahn-Banach extension theorem.

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  • Generalized Riesz potentials of functions in Morrey spaces L (1,φ;κ)(G) over non-doubling measure spaces

    Yoshihiro Sawano, Masaki Shigematsu, Tetsu Shimomura

    Forum Mathematicum  2020年3月  WALTER DE GRUYTER GMBH

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    開催年月日: 2020年3月    

    記述言語:英語  

    This paper proves the boundedness of the generalized Riesz potentials I ρ, μ, τ ⁢ f {I_{\rho,\mu,\tau}f} of functions in the Morrey space L (1, φ; κ) ⁢ (G) {L^{(1,\varphi;\kappa)}(G)} over a general measure space X, with G a bounded open set in X (or G is X) {X)}, as an extension of earlier results. The modification parameter τ is introduced for the purpose of including the case where the underlying measure does not satisfy the doubling condition. What is new in the present paper is that ρ depends on x ∈ X {x\in X}. An example in the end of this article convincingly explains why the modification parameter τ must be introduced.

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  • Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over quasi-metric measure spaces

    Daiki Hashimoto, Yoshihiro Sawano, Tetsu Shimomura

    Colloquium Mathematicum  2020年 

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    開催年月日: 2020年    

    Our aim in this paper is to give a Gagliardo-Nirenberg inequality for generalized Riesz potentials Iρ,µ,κf of functions in Musielak-Orlicz spaces over quasimetric measure spaces, as an extension of work of Mizuta et al. (2012). What is new in this paper is that ρ depends on (Formula Presented) and that the underlying measure µ is not doubling.

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  • Weighted local morrey spaces

    Shohei Nakamura, Yoshihiro Sawano, Hitoshi Tanaka

    Annales Academiae Scientiarum Fennicae Mathematica  2020年 

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    開催年月日: 2020年    

    We discuss the boundedness of linear and sublinear operators in two types of weighted local Morrey spaces. One is defined by Natasha Samko in 2008. The other is defined by Yasuo Komori-Furuya and Satoru Shirai in 2009. We characterize the class of weights for which the Hardy-Littlewood maximal operator is bounded. Under a certain integral condition it turns out that the singular integral operators are bounded if and only if the Hardy-Littlewood maximal operator is bounded. As an application of the characterization, the power weight function [pipe] · [pipe] is considered. The condition on α for which the Hardy-Littlewood maximal operator is bounded can be described completely.

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  • Interpolation of Morrey spaces for general parameters 招待 国際会議

    澤野嘉宏

    International Conference on Function Spaces  2018年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Interpolation of Morrey spaces 招待 国際会議

    澤野嘉宏

    2018 Beijing Conference on Harmonic Analysis and its Applications  2018年6月 

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  • Interpolation of Morrey spaces 招待 国際会議

    澤野嘉宏

    OTHA-2018 conference  2018年4月 

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  • Morrey spaces--Introduction 招待

    澤野嘉宏

    広島大学談話会  2017年11月 

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  • Introduction of Morrey spaces 招待 国際会議

    澤野嘉宏

    ISAAC国際会議  2017年8月 

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    記述言語:英語   会議種別:口頭発表(基調)  

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  • An obsevation of the atomic decomposition of Hardy spaces with variable exponent 招待 国際会議

    澤野嘉宏

    Harmonic Analysis and Applications at Tokyo 2017  2017年8月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Interpolation of Morrey spaces 招待 国際会議

    澤野嘉宏

    Banach spaces and operator theory with applications  2017年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Interpolation of diamond Morrey spaces 招待

    澤野嘉宏

    Harmonic Analysis and Applications at Beijing  2016年9月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Interpolation of diamond Morrey spaces 招待 国際会議

    澤野嘉宏

    4th East Asian Conference on Harmonic Analysis and Applications  2016年8月 

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  • Morrey Spaces--complex interpolations and weighted theory 招待 国際会議

    澤野嘉宏

    Harmonic Analysis and Applications at Matsumoto  2016年8月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey Spaces--complex interpolations and weighted theory 招待 国際会議

    澤野嘉宏

    調和解析と非線形偏微分方程式  2016年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey空間の複素補間について 招待

    澤野嘉宏

    京都大学数学教室談話会  2015年12月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Interpolation of Morrey spaces 招待 国際会議

    澤野嘉宏

    ザンジャン大学 数学セミナー  2015年9月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • A phase decomposition formula 招待 国際会議

    澤野嘉宏

    ISSAC CONFERENCE 2015  2015年8月 

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  • My Japanese book, Theory of Besov spaces, including a remark on the space ${\mathcal S}'/{\mathcal P}$ 招待

    澤野嘉宏

    ニコルスキー生誕110周年研究集会  2015年5月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Hardy spaces with variable exponents and generalized Campanato spaces 招待 国際会議

    澤野嘉宏

    Recent Advances in Variable Exponent Spaces and Non-linear Problems  2015年5月 

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  • Decompositions of Morrey spaces 招待 国際会議

    澤野嘉宏

    厦門大学 解析セミナー  2014年9月 

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    厦門大学 解析セミナー  2014年9月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Littlewood-Paley theory and Gagliardo-Nirenberg inequalities 招待 国際会議

    澤野嘉宏

    AIMS国際会議  2014年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Three remarks on Morrey spaces and related function spaces 招待 国際会議

    澤野嘉宏

    2nd East Asian Conference in Harmonic analysis and Applications  2014年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • An introduction to function spaces 招待

    澤野嘉宏

    福岡複素解析セミナー  2014年3月 

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  • An introduction to function spaces 招待

    澤野嘉宏

    城崎新人セミナー  2014年2月 

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  • Orlicz-Hardy spaces and their duals 招待 国際会議

    澤野嘉宏

    北京師範大学「関数空間とその応用の討論班」  2013年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    1st East Asian Conference in Harmonic analysis and Applications  2013年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • An observation on Hardy spaces 招待 国際会議

    澤野嘉宏

    Harmonic Analysis and its Application at Tokyo 2012  2012年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces 招待 国際会議

    澤野嘉宏

    The Erwin Schr\"{o}dinger International Institute for Mathematical Physics (Session ESI12)  2012年9月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Hardy spaces with variable exponents 招待 国際会議

    澤野嘉宏

    43回イラン数学会  2012年8月 

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    記述言語:英語   会議種別:口頭発表(基調)  

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  • Multilinear fractional integrals on Morrey spaces

    Takeshi Iida, Enji Sato, Yoshihiro Sawano, Hitoshi Tanaka

    Acta Mathematica Sinica, English Series  2012年7月 

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    記述言語:英語   会議種別:口頭発表(一般)  

    In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality. © 2012 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.

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  • Hardy spaces with variable exponents and generalized Campanato spaces 招待 国際会議

    澤野嘉宏

    SEAM28  2012年3月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Hardy spaces with variable exponents and generalized Campanato spaces 招待 国際会議

    澤野嘉宏

    浙江大学数学セミナー  2012年2月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Olsen's inequalities and their applications 招待 国際会議

    澤野嘉宏

    浙江教育大学数学セミナー  2012年2月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces with non-doubling measures II 招待 国際会議

    澤野嘉宏

    Harmonic Analysis and its Application at Nara  2011年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Sharp estimates of the modified Hardy-Littlewood maximal operator on the nonhomogeneous space via covering lemmas

    澤野嘉宏

    バンドン工科大学解析セミナー  2011年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Real Inversion Formulas of the Laplace Transform on Weighted Function Spaces 招待

    澤野嘉宏

    ラプラス変換の逆問題への応用  2011年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Hardy spaces with variable exponents and generalized Campanato spaces 招待 国際会議

    澤野嘉宏

    FSDONA2011  2011年9月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces for non-doubling measures 国際会議

    澤野嘉宏

    ISSAC CONFERENCE 2011  2011年8月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    Operators in Morrey Type Spaces and Applications  2011年5月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • New phase decomposition formula and its applications 招待

    澤野嘉宏

    国立中央大学解析セミナー  2010年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Singular integral inequalities and natural regularizations 招待

    澤野嘉宏

    Taiwan-Japan Joint Workshop on Inverse Problems  2010年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Olsen's inequality and its applications to Schr\"{o}dinger equations 招待

    澤野嘉宏

    京都大学研究集会「調和解析と偏微分方程式」  2010年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces for non-doubling measures 招待

    澤野嘉宏

    Mathematics colloquim at Macqarie  2010年1月 

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    記述言語:英語   会議種別:口頭発表(基調)  

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  • Br\'ezis-Gallou\"et-Wainger type inequalities in various function spaces 招待 国際会議

    澤野嘉宏

    Mini-conference on harmonic analysis  2009年12月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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  • Br\'ezis-Gallou\"et-Wainger type inequalities in various function spaces 招待 国際会議

    澤野嘉宏

    関数空間とその応用の討論班  2009年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • A note on the Olsen inequality 招待 国際会議

    澤野嘉宏

    関数空間とその応用の討論班  2009年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • ecompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces 招待 国際会議

    澤野嘉宏

    Harmonic Analysis and its Applications at Pohang  2009年11月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • A note on Morrey spaces 招待 国際会議

    澤野嘉宏

    インドネシアMalang大学 解析セミナー  2009年8月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Maximal operator for pseudo-differential operators with homogeneous symbols 招待

    澤野嘉宏

    京都大学談話会  2009年6月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • New phase decomposition formula and its applications 招待 国際会議

    澤野嘉宏

    Harmonic analysis and partial differential equations with applications  2009年5月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • 分数冪積分作用素の有界性について 招待

    澤野嘉宏

    齋藤三郎教授の最終講義  2009年1月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • A note on Olsen's inequality 招待 国際会議

    澤野嘉宏

    Analysis seminar, Geogia Institute of Technology  2008年12月 

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  • Maximal operator for pseudo-differential operators with homogeneous symbols 招待 国際会議

    澤野嘉宏

    Mini-conference on harmonic analysis  2008年11月 

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  • Maximal operator for pseudo-differential operators with homogeneous symbols 招待 国際会議

    澤野嘉宏

    Harmonic analysis and applications at Tokyo 2008  2008年10月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • ラプラス変換の実逆変換への再生核空間の応用 招待

    澤野嘉宏

    再生核の応用についての研究  2008年9月 

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    記述言語:日本語   会議種別:口頭発表(招待・特別)  

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  • Various boundedness of fractional integral operators 招待

    澤野嘉宏

    実函数論・函数解析学合同シンポジウム  2008年8月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Modulation spaces with $A_{\rm loc}^\infty$ weights, Second conference on pseudo-differential operators and related topics 招待 国際会議

    澤野嘉宏

    World Congress of Non-linear Analysis  2008年7月 

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  • Atomic decomposition for the weighted Morrey spaces 招待 国際会議

    澤野嘉宏

    調和解析と偏微分方程式  2007年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    SEAMS研究集会  2007年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Decompositions of the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces 国際会議

    澤野嘉宏

    Jena大学解析学セミナー  2007年6月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Sharp estimate of the modified maximal operator 国際会議

    澤野嘉宏

    Spring School on Analysisでのshort communication  2007年5月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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  • Functional differential equations of a type similar to $f(x)=2f(2x+1)-2f(2x-1)$ and its application to Poisson's equation

    澤野嘉宏, 米田剛

    数理解析研究所考究録  2007年 

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    21st MINI-CONFERENCE IN HARMONIC ANALYSIS  2006年11月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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  • Sharp maximal inequalities and commutators on Morrey spaces with non-doubling measures 招待 国際会議

    澤野嘉宏

    Third International Conference of Applied Mathematics  2006年8月 

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    ICM informal seminar  2006年8月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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  • Functional differential equations of a type similar to $f'(x)=2f(2x+1)-2f(2x-1)$ and its application to Poisson's equation 招待

    澤野嘉宏

    関数方程式の解のダイナミクスと数値シミュレーション  2006年7月 

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    記述言語:日本語   会議種別:口頭発表(招待・特別)  

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  • Non-doubling measureとMorrey空間に関して 招待

    澤野嘉宏

    日本数学会  2006年3月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • doubling条件を満たさない測度空間上のMorrey空間に関して

    澤野嘉宏, 田中仁

    数理解析研究所考究録  2006年 

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  • ある関数とクオーク分解に関して

    澤野嘉宏, 米田剛

    数理解析研究所考究録  2006年 

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  • doubling条件を満たさない測度上のMorrey空間に関して 招待 国際会議

    澤野嘉宏

    調和解析と非線形偏微分方程式  2005年7月 

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    記述言語:英語   会議種別:口頭発表(招待・特別)  

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  • Morrey spaces for non-doubling measures 招待 国際会議

    澤野嘉宏

    Seminari Analisi  2005年6月 

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    記述言語:英語   会議種別:口頭発表(一般)  

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▼全件表示

受賞

  • 建部賞(奨励賞)

    日本数学会  

    澤野嘉宏

共同研究・競争的資金等の研究課題

  • 平均振動量・増大度が一様でない関数空間の理論と応用

    研究課題/領域番号:21K03304  2021年4月 - 2026年3月

    日本学術振興会  科学研究費助成事業  基盤研究(C)  茨城大学

    中井 英一, 松岡 勝男, 堀内 利郎, 貞末 岳, 米田 剛, 澤野 嘉宏

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    配分額:4160000円 ( 直接経費:3200000円 、 間接経費:960000円 )

    今年度は、研究分担者や研究協力者との研究打合せ等は、すべて遠隔で行った。13th ISAAC Congress (ベルギー、遠隔開催)に招待され、Orlicz-Morrey 空間に関する講演を行った。また、ロシアで開催された国際研究集会「Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis X」に招待され、遠隔で参加して、Orlicz-Morrey 空間および弱 Orlicz-Morrey 空間に関する講演を行った。これらにより、海外の研究者とも研究情報の交換を行った。以下、今年度に得られた研究成果を列挙する。
    古典的な関数空間において確立されている H^1-BMO 双対性および VMO(CMO)-H^1 双対性の理論について、平均振動量が一様でない関数空間に拡張する試みが、すでに研究代表者らにより行われていたが、研究協力者によって完成した。さらに、これらの関数空間において、Riesz 変換や一般化分数べき積分作用素の有界性に関する結果を得て、理論を深めることができた。
    また、一般化 Young 関数を用いて Musielak-Orlicz-Hardy 空間を定義し、アトム分解およびウェーブレット分解による特徴づけを行った。
    重み付き Orlicz-Morrey 空間および弱 Orlicz-Morrey 空間上において、Hardy-Littlewood maximal 作用素や Calderon-Zygmund 作用素の有界性についての理論を構築した。
    Morrey 空間と弱 Morrey 空間上の掛算作用素(pointwise multiplier)について、これまで未知だった部分も含めて結果を得て、完全な特徴づけを完成させた。

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  • 特異積分と関数空間の研究(多重線形作用素の理論の深化)

    研究課題/領域番号:22K03393  2022年4月 - 2025年3月

    日本学術振興会  科学研究費助成事業  基盤研究(C)  東海大学

    古谷 康雄, 澤野 嘉宏, 松山 登喜夫

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    配分額:1950000円 ( 直接経費:1500000円 、 間接経費:450000円 )

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  • 調和解析における実関数論の方法とその応用

    研究課題/領域番号:20H01815  2020年4月 - 2025年3月

    日本学術振興会  科学研究費助成事業 基盤研究(B)  基盤研究(B)  東京女子大学

    宮地 晶彦, 古谷 康雄, 田中 仁, 冨田 直人, 筒井 容平, 澤野 嘉宏, 小林 政晴, 中井 英一

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    配分額:16120000円 ( 直接経費:12400000円 、 間接経費:3720000円 )

    多重線形の擬微分作用素でシンボルの導関数が決まった関数で抑えられるクラスの作用素に対して、新しいシンボルのクラスを導入し、これまで知られていたLebesgue空間での有界性を含む精密な結果を示した。この研究においては、アマルガム空間と呼ばれる関数空間とBrascamp-Lieb型不等式を利用することが重要な鍵となった。また3重線形Hilbert変換について、双線形の場合を単純に一般化した有界性は成り立たないことを示した。
    双線形の分数階積分作用素に対する重み付き評価について新しい不等式を得た。その不等式には2進立方体の直積に対するFefferman-Phong型不等式やCarleson型埋め込み不等式が密接に関係していることを示した。この研究にはスパース作用素が有効に利用された。関数のメディアンと最大関数に対する一般論を整備した。
    Morrey空間に関して、変動指数型Morrey空間の相対コンパクト集合の特徴付け、複素補間空間の性質、各点乗子となる関数の特徴付けについて、標準的な設定の下でこれまでに知られていた結果を、一般的な設定の下へ拡張した。また、分数階積分作用素や特異積分作用素のMorrey空間における評価も一般化した。
    非圧縮粘Navier-Stokes方程式をBesov空間で考察し、定常解の存在と安定性を示した。同じく非圧縮粘Navier-Stokes方程式を臨界のルベーグ空間においても考察し、弱解が強解になるための条件を得た。消散型偏微分方程式に対して、短時間Fourier変換を用いた解の表示を示し、それを用いてStrichartz型評価などを示した。

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  • 一般調和解析に由来する増大条件を伴う関数空間の深化と展開

    研究課題/領域番号:20K03663  2020年4月 - 2025年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  日本大学

    松岡 勝男, 水田 義弘, 中井 英一, 澤野 嘉宏

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    配分額:4420000円 ( 直接経費:3400000円 、 間接経費:1020000円 )

    増大条件を伴う関数空間のOrlicz versionと作用素の有界性について,増大条件を伴う非斉次central Morrey空間とそのOrlicz versionの適切な定義を導入するために、先ず増大条件を伴わない関数空間のOrlicz versionと作用素の有界性の共同研究「非斉次central Morrey-Orlicz空間上でのRieszポテンシャルの有界性」を海外協力者Lech Maligranda (Lulea University of Technology, Sweden; Poznan University of Technology, Poland) と始め、その結果が研究協力者Evgeniya Burtseva (Lulea University of Technology, Sweden) を加えた共著論文「Boundedness of the Riesz potential in central Morrey-Orlicz spaces」として雑誌 Positivity に最初 Online で掲載 (オープンアクセス) された。
    また、増大条件を伴う B_σ-関数空間と作用素の有界性について、増大条件を伴う B_σ-関数空間の適切な定義を導入するために、先ず増大条件を伴わない非斉次central Morrey空間とMorrey空間上でのd -modified Rieszポテンシャルの有界性の結果を統一する研究「d -modified Rieszポテンシャルの非斉次 B_σ-Morrey 空間上での有界性」を始め、その結果が論文「d -modified fractional integrals on B_σ-Morrey spaces」として雑誌 Rendiconti del Circolo Matematico di Palermo Series 2 に最初 Online で掲載された。
    上記に続く研究分担者中井英一との共同研究、研究分担者澤野嘉宏との共同研究については、大学における新型コロナウイルス感染拡大防止の措置により、すべてが昨年よりもわずかに進展している程度の状態であり、実績はまだまだ上がっていない状況である。
    そのような状況のなかで、研究分担者水田義弘により、Sobolev関数の増大性についての、研究分担者中井英一と澤野嘉宏により、Musielak-Orlicz Hardy 空間の特徴付けについての結果が得られている。

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  • 関数空間による数学解析の深化と発展

    研究課題/領域番号:19K03546  2019年4月 - 2022年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  首都大学東京

    澤野 嘉宏, 田中 仁, 岡田 正已

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    配分額:4420000円 ( 直接経費:3400000円 、 間接経費:1020000円 )

    研究成果が多岐にわたるので,箇条書きにして記載する。
    <BR>
    1.モレー空間の補間について研究し、さらにそれを楕円型偏微分方程式へと応用した。研究成果はMorrey spaces-Introduction and Applications to PDE I,IIとして出版予定である。2.直交ストリッカーツ評価についてローレンツ空間にの言葉で精密な評価を得た。3.モレー空間のジェームス定数について調べ,どのルベーグ空間と似ているかを検討した。4.ベゾフ空間と一般化モレー空間のサーベイを書いて研究成果をわかりやすくまとめた。5.種々の積分作用素,とくに分数べき積分作用素について,「双線形」,「一般距離空間」などの条件下で有界性を得ることができた。6.数列空間に作用する差分作用素のスペクトルを分類した。7.モジュラー不等式の成否を変動指数ルベーグ空間において調べた。8.楕円型微分作用素が生成する関数空間を考察し,その作用素が生成するリース変換の有界性をモレー空間において調べた。9.一般化モレー空間をサンプルとして,関数の分割理論を再考し,既存の理論を簡略化した。さらに,その応用として分数べき積分作用素の荷重付きの有界性を考察した。10.分数べき積分作用素のモレー空間の有界性について複素補間を用いて結果を精製した。この有界性はアダムスによって得られたもので,モレー空間にのみ着眼すると,アダムスの結果が最良であるとわかるが,補間という道具を用いて精製できることは意外であった。

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  • 特異積分と関数空間の研究(多重線形作用素のさらなる発展)

    研究課題/領域番号:19K03571  2019年4月 - 2022年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  東海大学

    古谷 康雄, 澤野 嘉宏, 松山 登喜夫

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    配分額:2340000円 ( 直接経費:1800000円 、 間接経費:540000円 )

    多重線形分数べき作用素の重み付き評価に関して3つの結果を得た.
    1. 多重線形分数べき作用素の重み付きL^p評価を得た.これによりCaffarelli-Kohn-Nirenbergの不等式の多重線形版を証明することができた.
    2. 2重線形分数べき作用素に関して,Moen の2016年の結果より弱い重みの条件でL^p有界性が成り立つことを証明することができた.応用として2重線形 Stein-Weiss の不等式を改良できた.
    3. 2重線形分数べき作用素に関して,重みを形を power weight に制限した場合にL^p有界になるための必要十分条件をみつけることができた.これは今まで知られていたApタイプの条件では有界性が成り立たないという反例も与えたことになる.

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  • Wienerの一般調和解析に端を発する関数空間の深化と展開

    研究課題/領域番号:17K05306  2017年4月 - 2021年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  日本大学

    松岡 勝男, 水田 義弘, 中井 英一, 澤野 嘉宏

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    配分額:4550000円 ( 直接経費:3500000円 、 間接経費:1050000円 )

    関数空間のOrlicz versionと作用素の有界性について、海外協力者のLech Maligranda (Lulea University of Technology, Sweden)と、共同研究「非斉次central Morrey-Orlicz空間上でのRieszポテンシャルの有界性」を昨年度から始め、異なる非斉次central Morrey-Orlicz空間上におけるHardy-Littlewood-Sobolev型の有界性のある程度の結果を得ていた。これに対して、研究協力者の古谷康雄 (東海大学) 等の論文「Fractional integral operators on central Morrey spaces, Math. Inequal. Appl., 20 (2017)」により、Hardy-Littlewood-Sobolev型のAdams型有界性はcentral Morrey空間上では成り立たないことが判明していたことから、急遽、Spann型有界性が成り立つための条件の妥当性の吟味が必要となり、その検討を始めることになった。
    一般化 Rieszポテンシャルとその有界性について、以前に得た非斉次central Morrey空間上での有界性を、非斉次central Campanato空間上の有界性に拡張することができた。そして、proceedings of IWOTA 2019に論文標題「d-modified Riesz potentials on central Campanato spaces」として掲載が決定された。また、研究分担者水田義弘との共同研究「変動指数central Morrey type 空間と一般化Rieszポテンシャルの弱有界性」の共著論文が、新たな研究協力者を得て完成し、雑誌Kyoto J. of Math. に掲載が決まった。

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  • 実関数論の方法による調和解析とその応用

    研究課題/領域番号:16H03943  2016年4月 - 2020年3月

    日本学術振興会  科学研究費助成事業 基盤研究(B)  基盤研究(B)  東京女子大学

    宮地 晶彦, 古谷 康雄, 田中 仁, 冨田 直人, 筒井 容平, 澤野 嘉宏, 小林 政晴

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    配分額:11180000円 ( 直接経費:8600000円 、 間接経費:2580000円 )

    多重線形の擬微分作用素の標準的なクラスにおいて、シンボルの微分可能性に関する精密な条件を得たこと、一般の関数を重みとするシンボルのクラスを導入しアマルガム空間での新たな有界性を証明したこと、などの成果があった。非負関数に対する不等式に関しては、多重線形分数階積分作用素に対する不等式やいくつかの最大関数の不等式に関して新たな結果を得た。また、種々の関数空間の性質を調べ、それらを応用して偏微分方程式の解析を行った。

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  • 実解析・調和解析に由来する関数空間の理論の深化と応用

    研究課題/領域番号:15H03621  2015年4月 - 2020年3月

    日本学術振興会  科学研究費助成事業 基盤研究(B)  基盤研究(B)  茨城大学

    中井 英一, 水田 義弘, 西垣 誠一, 堀内 利郎, 曾布川 拓也, 貞末 岳, 米田 剛, 澤野 嘉宏, 倉坪 茂彦, 藤間 昌一, 宮地 晶彦

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    配分額:16900000円 ( 直接経費:13000000円 、 間接経費:3900000円 )

    海外研究協力者 Dachun Yang 教授が開催する「International Conference on Harmonic Analysis and Its Applications (June 15-19, 2018, University of Chinese Academy of Sciences, Beijing, China)」に日本側代表者として参加した。また、研究分担者、研究協力者が合計8名参加した。38の講演があり、世界中から参加者も多く、活発な議論と研究情報の交換が行われた。
    国際研究集会「The 6th East Asian Conference in Harmonic Analysis and Applications (August 3--7, 2018, Osaka University)」に参加し、研究発表を行うとともに、最新の研究情報収集を行った。
    日本数学会の春と秋の学会、第57回実函数論・函数解析学合同シンポジウム、実解析学シンポジウム2018に参加、述べ9名の研究協力者を派遣し、研究発表を行うとともに最新の研究情報収集を行った。
    本年度の具体的な成果として、以下の研究成果が得られた。最大作用素および一般化分数べき積分作用素について、変動する振動量・増大度をもつカンパナト空間の元による掛け算作用素との交換子を考察し、変動する増大度をもつモリー空間において、この交換子がコンパクトであるための必要十分条件を与えた。オーリッツ空間および第3種オーリッツ・モリー空間上で、一般化分数べき積分作用素と一般化分数べき最大作用素の有界性に関する必要十分条件を得た。一般化分数べき積分作用素とカンパナト空間の元による掛け算作用素との交換子の有界性に関する必要十分条件をオーリッツ空間において与えた。弱オーリッツ空間における掛け算作用素を決定した。

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  • Conjectures associated with Brascamp-Lieb type inequalities

    研究課題/領域番号:16H05995  2016年4月 - 2019年3月

    日本学術振興会  科学研究費助成事業 若手研究(A)  若手研究(A)  埼玉大学

    BEZ NEAL, Bennett Jonathan, Cowling Michael, Cunanan Jayson, Flock Taryn, Gutierrez Susana, Iliopoulou Marina, Jeavons Chris, Lee Sanghyuk, 中村 昌平, 小澤 徹, 澤野 嘉宏, 杉本 充

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    配分額:13130000円 ( 直接経費:10100000円 、 間接経費:3030000円 )

    本研究の一つの重要な結果は非線形ブラスカンプ・リーブ(BL)予想の完全な証明に成功した事である。これは本研究の主な目的の一つで、一連の論文を通し達成する事ができた。最初に標準的なBL不等式の定数の局所有界性を示し、その結果を応用する事で任意に小さいソボレフの滑らかさをもつ関数に対する非線形BL予想を証明した。この安定性の結果の更なる応用として、多重線形フーリエ制限問題の理論を発展させた。次に、標準的なBL不等式の定数の連続性を証明し、それを用いる事によって非線形BL予想の完全な解決に成功した。更に、本研究では運動輸送方程式に関する評価を始めとする、様々な関連する理論を発展させる事に成功した。

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  • フーリエ解析学の新展開-関数空間の分割理論の深化と応用

    研究課題/領域番号:16K05209  2016年4月 - 2019年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  首都大学東京

    澤野 嘉宏, 田中 仁, 中村 昌平

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    担当区分:研究代表者  資金種別:競争的資金

    配分額:4420000円 ( 直接経費:3400000円 、 間接経費:1020000円 )

    今までの研究では特殊な条件でしかモレ―空間の閉部分空間は記述できなかったが,カルデロン積に着眼した本研究により任意のモレ―空間の対について複素補間空間が記述できた。また、関連する関数空間であるBesov空間の解説書「Theory of Besov spaces」をSpringerより出版した。この書籍には補間理論の最近の発展をモレー空間を含めて書いてある。

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  • 特異積分と関数空間の研究(多重線形作用素を視野に入れて)

    研究課題/領域番号:15K04938  2015年4月 - 2018年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  東海大学

    古谷 康雄, 澤野 嘉宏, 松山 登喜夫

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    配分額:3510000円 ( 直接経費:2700000円 、 間接経費:810000円 )

    多重線形作用素の様々な関数空間上での有界性を調べた.特にIα型とよばれる多重線形分数べき作用素の性質を調べた.ふつうの分数べき作用素は臨界指数 L1 においては弱い有界作用素にしか成り立たないが,この作用素は臨界指数においてもαに制限を加えると強い有界性が成り立つことを証明した.またこの作用素をradial関数に制限したときのセントラルモレー空間上での有界性も証明した.応用としてbilinear fractional integral に関する Stein-Weiss の不等式を改良した.

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  • 計算調和解析ー関数近似と離散表現

    研究課題/領域番号:24540184  2012年4月 - 2016年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  首都大学東京

    岡田 正已, 森藤 紳哉, 上野 敏秀, 澤野 嘉宏, 立澤 一哉

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    配分額:5070000円 ( 直接経費:3900000円 、 間接経費:1170000円 )

    不規則に配置された点での観測値から元々の関数を、よく再現する不規則サンプリングの方法を研究した。
    特に新しいのは、多次元ユークリッド空間内の無限に広がった不規則配置点上でのサンプリング近似における正定型関数を用いる方法を数学的に確証したことであり、その数理解析と近似誤差評価式の確立、さらに、その応用可能性について納得できる結果が得られたことである。
    理論的な側面では、整数格子点での古典的なサンプリング定理を、必ずしも帯域制限のない関数に適用できるように一般化したときの近似誤差評価と同じオーダーの近似度が得られることを示すことができた。そこでは、多変数の多項式近似についての新たな知見が鍵となった。

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  • 非線形発展方程式の凝縮現象と解の構造

    研究課題/領域番号:23224003  2011年4月 - 2016年3月

    日本学術振興会  科学研究費助成事業 基盤研究(S)  基盤研究(S)  京都大学

    堤 誉志雄, 岡本 久, 中西 賢次, 澤野 嘉宏, 岸本 展, 高岡 秀夫, 溝口 紀子, 前田 昌也, 加藤 孝盛, 宮路 智行, 佐々木 洋平

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    配分額:75010000円 ( 直接経費:57700000円 、 間接経費:17310000円 )

    非線形波動・分散型方程式に対して,中西はSchlagとともに,不安定な基底状態解の近傍から出発する解の大域的挙動を完全に決定することに成功した.従来,基底状態より高いエネルギー準位を持つ解については,ほとんど先行研究はなかったため大きな進展である.堤は吉川との共同研究により,形状記憶合金の等温Falkモデルに対して,2種類の不変測度を構成して比較した.岡本は東海林との共同研究で,張力重力波のストークスドリフトと呼ばれる現象を,数学的に解析するとともに数値計算により調べた.岡本と東海林は,張力重力波の場合でも,粒子運動の軌跡が閉曲線とならないことを複素函数論的な手法で証明した.

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  • 変動する指標をもつ関数空間を基礎とした調和解析とその応用

    研究課題/領域番号:24540159  2012年4月 - 2015年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  茨城大学

    中井 英一, 堀内 利郎, 曾布川 拓也, 貞末 岳, 澤野 嘉宏, 水田 義弘

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    配分額:5070000円 ( 直接経費:3900000円 、 間接経費:1170000円 )

    変動指数を持つハーディー空間、オーリッツ・ハーディー空間に関して、ポアソン積分、アトム分解、リトルウッド・ペイリー分解等による特徴付けを行い、特異積分作用素、分数べき積分作用素等についての有界性を得るとともに、関連する関数空間やその双対空間等の研究と合わせて、理論を完成することができた。また、振動・増大度が変動する関数空間としての一般化モリー・カンパナト空間、Bシグマ・モリー・カンパナト空間、そして、これらを統一した関数空間の理論を開拓した。これらを用いて具体的に偏微分方程式の解の解析を行った。さらに、マルチンゲール理論に関して調和解析的理論を構成した。

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  • 特異積分と関数空間の研究(偏微分方程式を視野に入れて)

    研究課題/領域番号:24540194  2012年4月 - 2015年3月

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  東海大学

    古谷 康雄, 澤野 嘉宏, 松山 登喜夫

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    配分額:3510000円 ( 直接経費:2700000円 、 間接経費:810000円 )

    多重線形分数冪作用素の直積Herz空間上での有界性を証明した.さらに臨界指数を超えた場合の評価も得た.Morrey空間,Herz 空間などを統一的に扱うことのできるB_sigma 空間を導入して,Hardy-Littlewood 最大作用素,特異積分作用素,分数冪積分作用素がその空間上で有界であることを証明した.分数冪作用素の評価に関して,MuckenhouptとWheeden は重みつき Lp → Lq 有界性を示した.AdamsはMorrey 空間上での有界性を示した.我々は重みつきMorrey空間上での有界性を示した.この結果は既知の結果をすべて統合するものである.

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  • 調和解析の数学一般への応用

    研究課題/領域番号:24740085  2012年4月 - 2015年3月

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)  首都大学東京

    澤野 嘉宏

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    担当区分:研究代表者  資金種別:競争的資金

    配分額:4420000円 ( 直接経費:3400000円 、 間接経費:1020000円 )

    本研究の成果は以下のものに大別される。1.種々の関数空間に属する関数のアトム分解について考察した。2.ベゾフ空間やトリーベル・リゾルキン空間における基本性質として良く知られている命題の証明を与えた。この基本性質は多くの書籍、論文に書かれているが明確な証明は知られていなかった。3.モレー空間とその周辺の種々の関数空間の性質を調べた。4.再生核ヒルベルト空間を用いたディラックのデルタの構成方法を試みた。

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  • 実関数論的手法による調和解析とその応用

    研究課題/領域番号:23340034  2011年4月 - 2015年3月

    日本学術振興会  科学研究費助成事業 基盤研究(B)  基盤研究(B)  東京女子大学

    宮地 晶彦, 岡田 正已, 古谷 康雄, 菊池 万里, 田中 仁, 冨田 直人, 澤野 嘉宏, 中井 英一, 筒井 容平, 佐藤 秀一, 小林 政晴, 立澤 一哉

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    配分額:18070000円 ( 直接経費:13900000円 、 間接経費:4170000円 )

    双線形フーリエ乗子作用素のルベーグ空間およびハーディ空間での有界性の十分条件となるヘルマンダー=ミーリン型条件に対して、直積型ソボレフ・ノルムを用いた場合の臨界の滑らかさの指数を決定した。線形の擬微分作用素に対するカルデラン=バイランクールの定理の双線形作用素への一般化にあたる定理を示した。調和解析に現れる最大作用素などの種々の作用素について、種々の関数空間での新しい評価を得た。

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  • 非線形波動・分散型方程式の幾何学的対称性と弱解の構造

    研究課題/領域番号:23244012  2011年    

    日本学術振興会  科学研究費助成事業 基盤研究(A)  基盤研究(A)  京都大学

    堤 誉志雄, 重川 一郎, 國府 寛司, 中西 賢次, 大鍛治 隆史, 澤野 嘉宏

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    配分額:12350000円 ( 直接経費:9500000円 、 間接経費:2850000円 )

    研究分担者の中西はシカゴ大学のSchlag氏とともに,非線形波動方程式および非線形シュレディンガー方程式に対し,基底状態の近傍にある解の大域的挙動を研究した.同氏が1999年に開発したMorawetz型の評価式とKenig-Merleによって提唱された最小爆発解論法をあわせることにより,基底状態よりエネルギー準位が高い解に対しても,大域的漸近挙動を決定することに成功した.基底状態の近傍とはいえ,基底状態よりエネルギーが高い一般解の大域的漸近挙動を決定した研究はこれが初めてである.
    また,研究代表者の堤は,数理解析研究所の宮路智行氏および広島大学の大西勇氏と共同で,Lugiato-Lefever方程式の定常解の漸近安定性を研究した.Lugiato-Lefever方程式は,定数外力と減衰項を持つ非線形シュレディンガー方程式であり,ハミルトン系としての構造を持たないため,従来の研究方法は必ずしも有効ではなかった.非線形放物型方程式の場合,解析半群の正則性と生成作用素の分数べきの理論を適用することにより,定常解の漸近安定性が得られていた.しかし,これらの理論は非線形波動・分散型方程式に対しては適用できない.今回は,定常解の近傍における線形化作用素の精密な解析を行ない,複素ポテンシャルを持つ線形シュレディンガー方程式に対するStrichartz評価式を証明することにより漸近安定性の証明に成功した.

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  • 調和解析の数学一般への応用

    研究課題/領域番号:21740104  2009年 - 2011年

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)  京都大学

    澤野 嘉宏

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    担当区分:研究代表者  資金種別:競争的資金

    配分額:4420000円 ( 直接経費:3400000円 、 間接経費:1020000円 )

    次の研究課題に取り組んだ.課題1.モレー空間における分数べき積分作用素の多重線形評価と偏微分方程式への応用課題2.変動指数を備えているハーディー空間課題3.公理に基づいたベゾフ空間の解析課題4.再生核ヒルベルト空間の英語の著書の執筆課題5.ベゾフ空間論の日本語の著書の作成.
    1.モレー空間における分数べき積分作用素の多重線形評価と偏微分方程式への応用課題
    2.変動指数を備えているハーディー空間課題
    3.公理に基づいたベゾフ空間の解析課題
    4.再生核ヒルベルト空間の英語の著書の執筆課題
    5.ベゾフ空間論の日本語の著書の作成.

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  • 変動する指標をもつ関数空間

    研究課題/領域番号:20540167  2008年 - 2011年

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C) 

    中井 英一, 水田 義弘, 貞末 岳, 澤野 嘉宏

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    配分額:4290000円 ( 直接経費:3300000円 、 間接経費:990000円 )

    「変動する指標をもつ関数空間」の理論を構築するため、これまでの「変動指数をもつLebesgue空間」に関する研究を踏まえ、「変動指数をもつHardy空間」および「変動増大度をもつ一般化Campanato空間」とそれらに関連した種々の関数空間について詳しく調査を行った。これらの関数空間の適切な定義を見つけ、そこでの種々の積分作用素の振る舞いを調べることを通して、理論が構築できた。

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  • 実解析学における関数空間の研究および偏微分方程式への応用

    研究課題/領域番号:07J00483  2007年 - 2009年

    日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費  首都大学東京

    澤野 嘉宏

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    配分額:2200000円 ( 直接経費:2200000円 )

    本年後は次の研究をした。
    1.Non-doubling測度を備えたユークリッド空間の解析
    2.Lebesgue測度空間を備えたユークリッド空間、コンパクトリーマン多様体上の関数空間の解析
    3.再生各ヒルベルト空間に関する解析
    1.私が定義したMorrey空間predualを決定して、Morrey空間および周辺の関数空間を整備した。広島大学、バンドン工科大学でこの関数空間に関して講義した。
    2.昨年得られたアトム分解などを用いて領域上の関数空間(Besov-Morrey空間など)の理論を展開し、その応用としてコンパクトリーマン多様体上の関数空間の解析を展開した。
    アトム分解のそのほかの応用として擬微分作用素を考えて、Harmonic Analysis and its Application at Sapporo-2007の報告集にまとめた。さらに、Morreyノルムの同値なノルムとしてTriebel-Lizorkin-Morreyノルムがあるということもその報告集に収録した。Besov空間と類似の関数空間であるModulation空間に関してアトム分解を考えた。さらに、その結果は荷重つきの関数空間に拡張できることを示した。
    3.ラプラス変換の逆変換公式を求めるべく、再生核Hibert空間H_Kを考察し(Kを特定してH_Kを記述しなくてはならないが、定義はここでは省略)ある種の積分作用素のコンパクト性を示した。
    また、特異積分作用素を数値的に計算するときに近似法が有効であり、誤差評価を与えた。

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  • 実関数論の手法による調和解析とその応用

    研究課題/領域番号:18340043  2006年 - 2009年

    日本学術振興会  科学研究費助成事業  基盤研究(B)  東京女子大学

    宮地 晶彦, 勘甚 裕一, 小薗 英雄, 佐藤 秀一, 佐藤 圓治, 古谷 康雄, 立澤 一哉, 篠原 昌彦, 大阿久 俊則, 岡田 正已, 杉本 充, 冨田 直人, 小林 政晴, 澤野 嘉宏, 中井 英一, 勘甚 裕一, 佐藤 圓治

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    配分額:15130000円 ( 直接経費:12400000円 、 間接経費:2730000円 )

    フェファーマン-スタインによるハーディー空間と同様の性質を持つ関数空間をユークリッド空間の領域上に導入し,その性質を確立した.この関数空間は,或る条件をみたす微分同相写像の定める変数変換によって,同種の関数空間に変換されるという性質を持つ.この関数空間を古典的直交級数の研究に応用した.時間周波数解析など実関数論的調和解析に現れるいくつかの関数空間の性質を調べ,それらの空間での作用素についての結果を得た.

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  • 実解析学における関数空間の研究と偏微分方程式への応用

    2007年4月 - 2008年3月

    日本学術振興会  特別研究員奨励費 

    澤野嘉宏

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    担当区分:研究代表者  資金種別:競争的資金

    微分積分を中心とした解析学全般の研究

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  • 実解析学における関数空間の研究および偏微分方程式への応用

    2006年4月 - 2007年3月

    日本学術振興会  特別研究員奨励費 

    澤野嘉宏

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    担当区分:研究代表者  資金種別:競争的資金

    調和解析に現れる作用素の研究をしている.

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▼全件表示

担当経験のある科目(授業)

  • 整数論演習

    機関名:学習院大学

  • 微分積分演習

    機関名:首都大学東京、学習院大学

  • 関数解析

    機関名:学習院大学

  • 微分積分

    機関名:首都大学東京

  • 関数解析

    機関名:首都大学東京

  • 調和解析学

    機関名:山形大学,ユーラシア中央大学,首都大学東京,広島大学,京都大学

  • 微分積分

    機関名:学習院大学,京都大学,首都大学東京

  • 関数解析

    機関名:学習院大学,京都大学,首都大学東京

  • 複素解析

    機関名:学習院大学,京都大学,首都大学東京

  • フーリエ解析

    機関名:京都大学,首都大学東京

  • 確率論

    機関名:明治大学,首都大学東京

  • 常微分方程式

    機関名:明治大学,首都大学東京

  • ベクトル解析

    機関名:学習院大学,首都大学東京

  • ルベーグ積分

    機関名:学習院大学,京都大学,首都大学東京

▼全件表示

委員歴

  • 2019年7月 - 現在

    Journal of Fourier Analysisのエディター  

  • 2014年4月 - 現在

    Azerbaijan Journal of Mathematics編集委員  

  • 2013年7月 - 現在

    Journal of Function Spaces編集委員  

  • 2013年4月 - 現在

    Journal of Analysis and Applications編集委員  

  • 2016年4月 - 2018年3月

    TJM(Tokyo Journal of Mathematics)編集委員  

  • 2015年7月 - 2017年6月

    日本数学会   「数学」編集委員  

  • 2013年4月 - 2016年4月

    World Scientific Journal編集委員  

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社会貢献活動

  • 中央大調和解析セミナー組織委員

    役割:運営参加・支援

    2016年 - 現在

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  • 研究指導

    役割:助言・指導

    イラン,ザンジャン大学  2017年 - 2018年

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  • 紙を使って放物線を作ろう

    役割:講師

    首都大学東京  2017年7月 -  

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  • 研究委託指導

    役割:助言・指導

    パキスタン,チュビリシー大学  2016年 - 2017年

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  • 実函数論・函数解析学合同シンポジウム

    役割:運営参加・支援

    2016年9月    

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  • 東京大学調和解析セミナー組織委員

    役割:運営参加・支援

    2012年 - 2016年

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  • 不等式入門,最大最小問題へのアプローチ

    役割:講師

    首都大学東京  2016年 -  

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  • 不等式入門,最大最小問題へのアプローチ

    役割:講師

    2015年7月 -  

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  • ルベーグ積分入門

    役割:講師

    首都大学東京  2014年10月 - 2014年11月

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    種別:出前授業

    researchmap

  • 研究者としてやっていくためには,回顧と分析

    役割:講師

    2014年4月 -  

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  • 研究者としてやっていくためには

    役割:講師

    トルコ,クルシェヒール,Ahi Evran University  2014年3月 -  

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  • 測度0の図形とその性質

    役割:講師

    首都大学東京  2014年 -  

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  • 研究者としてやっていくためには,回顧と分析

    役割:講師

    首都大学東京  2013年4月 -  

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  • 不等式入門,

    役割:講師

    首都大学東京  2012年6月 -  

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  • 京都大学NLPDEセミナー

    役割:運営参加・支援

    京都大学  2010年4月 - 2012年3月

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  • フェルマーの最終定理について

    役割:講師

    京都大学  2011年8月 -  

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  • 調和解析入門

    役割:講師

    首都大学東京 

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  • 研究資金の審査

    役割:報告書執筆

    香港 

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