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A study on wavelets and function spaces with variable exponent based on real analysis

Research Project

Project/Area Number 15K04928
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionTokyo City University (2019-2022)
Okayama University (2015-2018)

Principal Investigator

Izuki Mitsuo  東京都市大学, 共通教育部, 准教授 (80507179)

Project Period (FY) 2015-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywordsウェーブレット / 変動指数 / Muckenhouptの理論 / BMO / Muckenhouptの荷重 / モジュラー不等式 / John-Nirenbergの不等式 / Herz空間 / Bergman変換 / 変動指数解析 / 1変数複素解析
Outline of Final Research Achievements

One of the important result is a study on Herz spaces with variable exponents joint work with Professor Takahiro Noi. We have constructed a method which shows boundedness of some fundamental operators on function spaces involving variable exponent and Muckenhoupt weight. In addition, we have defined a new Hardy Space associated to critical Herz spaces with variable exponent and proved some basic properties of the space. Additionally we have defined two weighted Herz spaces with variable exponents and given equivalent norms. As a result, we have constructed a basic analysis method on those spaces.
One of the another result is a joint work with Professor Yoshihiro Sawano, Doctor Toru Nogayama and Professor Takahiro Noi, which have obtained several results on local Muckenhoupt weights with variable exponent and corresponding function spaces.

Academic Significance and Societal Importance of the Research Achievements

今後、より多くの自然現象の数学モデル化や工学における諸分野におけるウェーブレット理論や変動指数解析の応用を進めていく上で、その枠組みとなる多用な関数空間が求められることになります。Herz空間において、変動指数とMuckenhoupt荷重の理論を用いて変動指数型の荷重つきの新たな関数のクラスを複数定義してそれらの性質を明らかにできたこと、実解析における最新の理論ともいえる局所変動指数型Muckenhouptの荷重理論の研究に取り組み、その荷重と変動指数の両方をもつ幾つかの関数空間において一定の成果を得られたことは大変意義があります。

Report

(9 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (24 results)

All 2022 2021 2020 2019 2018 2017 2016 2015

All Journal Article (19 results) (of which Peer Reviewed: 19 results,  Open Access: 17 results,  Acknowledgement Compliant: 6 results) Presentation (5 results) (of which Int'l Joint Research: 1 results,  Invited: 5 results)

  • [Journal Article] Wavelet characterization of local Muckenhoupt weighted Sobolev spaces with variable exponents2022

    • Author(s)
      出耒光夫,野ケ山徹,野井貴弘,澤野嘉宏
    • Journal Title

      CONSTRUCTIVE APPROXIMATION

      Volume: 21 Issue: 01 Pages: 1-59

    • DOI

      10.1007/s00365-022-09573-6

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016916

    • Related Report
      2022 Annual Research Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [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 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent2020

    • Author(s)
      出耒光夫,野ケ山徹,野井貴弘,澤野嘉宏
    • Journal Title

      Nonlinear Analysis

      Volume: 198 Pages: 1-13

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Two Weighted Herz Spaces with Variable Exponents2019

    • Author(s)
      出耒光夫, 野井貴弘
    • Journal Title

      Bulletin of the Malaysian Mathematical Sciences Society

      Volume: 43 Pages: 169-200

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The John-Nirenberg inequality in ball Banach function spaces and application to characterization of BMO2019

    • Author(s)
      出耒光夫, 野井貴弘, 澤野嘉宏
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 268 Pages: 1-11

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces on domains2019

    • Author(s)
      出耒光夫, 野井貴弘
    • Journal Title

      Mathematische Nachrichten

      Volume: 292 Pages: 2212-2251

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Some Modular Inequalities in Lebesgue Spaces with Variable Exponent on the Complex Plane2019

    • Author(s)
      出耒光夫, 小山剛史, 野井貴弘, 澤野嘉宏
    • Journal Title

      Mathematical Notes

      Volume: 106 Pages: 229-234

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Some modular inequalities in Lebesgue spaces with variable exponent on the complex plane2019

    • Author(s)
      Mitsuo Izuki, Takeshi Koyama, Takahiro Noi, and Yoshihiro Sawano
    • Journal Title

      Mathematical Notes

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] A simple estimate of the Bloch constant2018

    • Author(s)
      Mitsuo Izuki, Takeshi Koyama, Takahiro Noi, and Tatsuki Takeuchi
    • Journal Title

      Communications in Mathematical Analysis

      Volume: 21 Pages: 35-41

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An elementary proof of the Caratheodory kernel convergence theorem2018

    • Author(s)
      Mitsuo Izuki and Takeshi Koyama
    • Journal Title

      Azerbaijan Journal of Mathematics

      Volume: 8 Pages: 69-85

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterization of BMO via ball Banach function spaces2017

    • Author(s)
      Mitsuo Izuki, Yoshihiro Sawano
    • Journal Title

      Vestnik Sankt-Peterburgskogo Universiteta. Matematica Mekhanika. Astronomiya

      Volume: 4(62) Pages: 78-86

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An intrinsic square function on weighted Herz spaces with variable exponent2017

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      Journal of Mathematical Inequalities

      Volume: 11 Pages: 799-816

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Complex interpolation of grand Lebesgue spaces2017

    • Author(s)
      Denny Ivanal Hakim, Mitsuo Izuki and Yoshihiro Sawano
    • Journal Title

      Monatshefte fur Mathematik

      Volume: 184 Pages: 245-272

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterization of BMO via ball Banach function spaces2017

    • Author(s)
      Mitsuo Izuki, Yoshihiro Sawano
    • Journal Title

      Vestnik St. Petersburg University: Mathematics

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Boundedness of fractional integrals on weighted Herz spaces with variable exponent,2016

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 199 Pages: 1-16

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Hardy spaces associated to critical Herz spaces with variable exponent2016

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      Mediterranean Journal of Mathematics

      Volume: 13 Pages: 2981-3013

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] The Hardy{Littlewood maximal operator on some critical weighted Herz spaces with variable exponent2016

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      Jaen Journal on Approximation

      Volume: 8 Pages: 97-112

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Another proof of characterization of BMO via Banach function spaces2016

    • Author(s)
      Mitsuo Izuki
    • Journal Title

      Revista de la Union Matematica Argentina

      Volume: 57 Pages: 103-109

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent2015

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

      Annales Academia Scientiarum Fennica Mathematica

      Volume: 40 Pages: 551-571

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] ウェーブレット係数による解析関数の特徴付け2019

    • Author(s)
      出耒 光夫
    • Organizer
      東京都市大学 調和解析セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Banach 関数空間による BMO ノルムの一般化2019

    • Author(s)
      出耒 光夫
    • Organizer
      東京都市大学 調和解析セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 変動指数解析の近年の発展と課題2018

    • Author(s)
      出耒 光夫
    • Organizer
      RIMS共同研究「関数空間の一般化とその周辺」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Characterization of BMO via Banach function spaces2015

    • Author(s)
      Mitsuo Izuki
    • Organizer
      Harmonic Analysis and its Applications in Tokyo 2015
    • Place of Presentation
      早稲田大学
    • Year and Date
      2015-11-28
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] An intrinsic square function on weighted Herz spaces with variable exponent2015

    • Author(s)
      出耒光夫
    • Organizer
      調和解析駒場セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2015-07-11
    • Related Report
      2015 Research-status Report
    • Invited

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Published: 2015-04-16   Modified: 2024-01-30  

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