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A refinement and development of mathematical analysis by means of function spaces

Research Project

Project/Area Number 19K03546
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionChuo University (2020-2021)
Tokyo Metropolitan University (2019)

Principal Investigator

Sawano Yoshihiro  中央大学, 理工学部, 教授 (40532635)

Co-Investigator(Kenkyū-buntansha) 田中 仁  筑波技術大学, 障害者高等教育研究支援センター, 講師 (70422392)
岡田 正已  東京都立大学, 理学研究科, 客員研究員 (00152314)
飯田 毅士  福島工業高等専門学校, 一般教科, 准教授 (60633435)
中村 昌平  大阪大学, 理学研究科, 助教 (30896121)
Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsモレー空間 / ベゾフ空間 / 補間理論 / 分数べき積分作用素 / 複素補間 / sparse分解 / コンパクト性 / 関数空間
Outline of Research at the Start

田中仁氏による分数べき積分作用素の解析,岡田正已氏によるカントロビッチ作用素の解析を踏まえてコンパクト予想を否定的に解決する。その過程で得られた研究成果を偏微分方程式に応用する。また,中村昌平氏,Denny Ivanal Hakim氏,Giuseppe di Fazio氏と共同で「Morrey spaces--Application to integral operators」という書籍を書き上げる。

Outline of Final Research Achievements

I investigated the interpolation. Roughly speaking, there are two types of interpolations, complex/real. Among others, I investigated the complex interpolation. My experience shows that Morrey spaces are useful when we consider counterexamples of some facts. I obtained an interpolation formula that does not fall within the scope of the known results by means of variable exponents. This result is already published. Another important fact is that complex interpolation is useful to obtain a non-trivial result.

Academic Significance and Societal Importance of the Research Achievements

複素補間は作用素の補間に有効であるというのが今までの常識であったが,その背景にはカルデロン積があり、それを計算することで自明ではない結果を得ることができることが分かった。具体的にはBourgainの考察した関数空間と弱ルベーグ空間との非自明な包含関係を複素補間により得ることができたことは大きい。つまり、補間理論としてよく使われる公式以外に、補間理論自体が内包している多くの情報を引き出す試みがうまくいったことになる。

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (26 results)

All 2022 2021 2020 2019 Other

All Int'l Joint Research (5 results) Journal Article (13 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 13 results,  Open Access: 8 results) Presentation (5 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results) Book (2 results) Remarks (1 results)

  • [Int'l Joint Research] バンドン工科大学(インドネシア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] 高等科学研究所(イラン)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] カターニア大学(イタリア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] モスクワ友情大学(ロシア連邦)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Adams Miekiewicz University(ポーランド)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Boundedness of composition operators on reproducing kernel Hilbert spaces with analytic positive definite functions2022

    • Author(s)
      Ikeda Masahiro、Ishikawa Isao、Sawano Yoshihiro
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 511 Issue: 1 Pages: 126048-126048

    • DOI

      10.1016/j.jmaa.2022.126048

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Atomic and wavelet characterizations of Musielak-Orlicz Hardy spaces for generalized Orlicz functions2021

    • Author(s)
      Izuki Mitsuo、Nakai Eiichi、Sawano Yoshihiro
    • Journal Title

      Integral Equations and Operator Theory

      Volume: 21 Issue: 02 Pages: 1-34

    • DOI

      10.1007/s00020-021-02672-2

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016917

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex interpolation of variable Morrey spaces2021

    • Author(s)
      Hakim Denny Ivanal、Sawano Yoshihiro
    • Journal Title

      Mathematische Nachrichten

      Volume: 294 Issue: 11 Pages: 2140-2150

    • DOI

      10.1002/mana.202000513

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Fractional Maximal Operator on Musielak?Orlicz Spaces Over Unbounded Quasi-Metric Measure Spaces2021

    • Author(s)
      Sawano Yoshihiro、Shimomura Tetsu
    • Journal Title

      Results in Mathematics

      Volume: 76 Issue: 4 Pages: 1-18

    • DOI

      10.1007/s00025-021-01490-7

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Weighted Hankel Transform and Its Applications to Fourier Transform2021

    • Author(s)
      Okada Masami、Sawano Yoshihiro
    • Journal Title

      Journal of Fourier Analysis and Applications

      Volume: 27 Issue: 2 Pages: 1-28

    • DOI

      10.1007/s00041-021-09831-4

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Complex Interpolation and the Adams Theorem2020

    • Author(s)
      Sawano Yoshihiro、Sugano Satoko
    • Journal Title

      Potential Analysis

      Volume: 54 Issue: 2 Pages: 299-305

    • DOI

      10.1007/s11118-020-09827-7

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Weighted local Morrey spaces2020

    • Author(s)
      Nakamura Shohei、Sawano Yoshihiro、Tanaka Hitoshi
    • Journal Title

      Annales Academiae Scientiarum Fennicae Mathematica

      Volume: 45 Issue: 1 Pages: 67-93

    • DOI

      10.5186/aasfm.2020.4504

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Paracontrolled quasi-geostrophic equation with space-time white noise2020

    • Author(s)
      Inahama Yuzuru、Sawano Yoshihiro
    • Journal Title

      Dissertationes Mathematicae

      Volume: 558 Pages: 1-81

    • DOI

      10.4064/dm806-7-2020

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Weak Type Vector-Valued Inequality for the Modified Hardy-Littlewood Maximal Operator for General Radon Measure on Rn2020

    • Author(s)
      Sawano Yoshihiro
    • Journal Title

      Analysis and Geometry in Metric Spaces

      Volume: 8 Issue: 1 Pages: 261-267

    • DOI

      10.1515/agms-2020-0113

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Homogeneous Besov spaces2020

    • Author(s)
      Sawano Yoshihiro
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 60 Issue: 1 Pages: 1-43

    • DOI

      10.1215/21562261-2019-0038

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex interpolation of the predual of Morrey spaces over measure spaces2019

    • Author(s)
      Burenkov Victor I.、Hakim Denny I.、Nakai Eiichi、Sawano Yoshihiro、Sobukawa Takuya、Tararykova Tamara V.
    • Journal Title

      Georgian Mathematical Journal

      Volume: 0 Issue: 3 Pages: 341-348

    • DOI

      10.1515/gmj-2019-2070

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A thought on generalized Morrey spaces2019

    • Author(s)
      Yoshihiro Sawano
    • Journal Title

      J. Indones. Math. Soc.

      Volume: 25 Pages: 210-281

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex interpolation and Calderon-Mityagin couples of Morrey spaces2019

    • Author(s)
      Mieczyslaw Mastylo and Yoshihiro Sawano
    • Journal Title

      Analysis and PDE

      Volume: 12 Issue: 7 Pages: 1711-1740

    • DOI

      10.2140/apde.2019.12.1711

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] 局所正則荷重について2021

    • Author(s)
      澤野嘉宏
    • Organizer
      北京師範大学連続公演
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Weighted Hankel Transform and Its Applications to Fourier Transform2021

    • Author(s)
      澤野嘉宏
    • Organizer
      調和解析セミナー
    • Related Report
      2020 Research-status Report
  • [Presentation] Morrey spaces2020

    • Author(s)
      澤野嘉宏
    • Organizer
      Harmonic and Spectral Analysis 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Morrey spaces2020

    • Author(s)
      澤野嘉宏
    • Organizer
      ICOMCOS
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] モレー空間の閉部分空間について2019

    • Author(s)
      澤野嘉宏
    • Organizer
      実解析シンポジウム
    • Related Report
      2019 Research-status Report
  • [Book] 調和解析への招待2022

    • Author(s)
      澤野 嘉宏
    • Total Pages
      168
    • Publisher
      サイエンス社
    • ISBN
      9784781915388
    • Related Report
      2021 Annual Research Report
  • [Book] Introduction and Applications to Integral Operators and PDE’s, Volume I+II2020

    • Author(s)
      Yoshihiro Sawano, Giuseppe Di Fazio and Denny Ivanal Hakim
    • Total Pages
      940
    • Publisher
      CRC press
    • Related Report
      2020 Research-status Report
  • [Remarks] 澤野嘉宏のホームページ

    • URL

      https://www.math.chuo-u.ac.jp/sawano/

    • Related Report
      2020 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2023-01-30  

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