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Study of the operators on some function spaces in harmonic analysis

Research Project

Project/Area Number 26400129
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionYamagata University

Principal Investigator

SATO ENJI  山形大学, 理学部, 名誉教授 (80107177)

Co-Investigator(Kenkyū-buntansha) 古谷 康雄  東海大学, 理学部, 教授 (70234903)
Co-Investigator(Renkei-kenkyūsha) KOBAYASHI Masaharu  北海道大学, 理学研究院, 准教授 (30516480)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords分数冪積分作用素 / モレー空間 / フーリエマルチプライヤー / モジュレーション空間 / 双線形作用素 / モリー空間 / ラデアル関数 / フーリエマルチプライヤー作用素 / 移転定理 / Lp空間 / アダムスの不等式 / 重み関数
Outline of Final Research Achievements

Study of the operators in function spaces by harmonic analysis is very effective for partial differentiable equations. Moreover, it is important that an operator in some function spaces is bounded. Main subjects in our research are study of Fourier multiplier operators, study of fractional integral operators in Morrey spaces, and study of modulation spaces which are related to partial differential equations. First, we gave a simple proof of the restriction theorem of Fourier multipliers, and generalized the result of the fractional integral operators in Morrey spaces. Also we developed the result in modulation spaces by the study of operating functions.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (5 results)

All 2017 2016 2015 2014

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (3 results) (of which Invited: 2 results)

  • [Journal Article] Fractional integral operators on central Morrey spces2017

    • Author(s)
      Yasuo Komori-Furuya, Enji Sato
    • Journal Title

      Mathematical Inequalities and Applications

      Volume: 未定

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on the restriction theorems for the maximal operators on Rd2015

    • Author(s)
      Enji Sato
    • Journal Title

      Analysis in Theory and Applications

      Volume: 31 Issue: 2 Pages: 123-137

    • DOI

      10.4208/ata.2015.v31.n2.3

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] Morrey spaces related to radial functions2017

    • Author(s)
      佐藤圓治
    • Organizer
      調和解析セミナー2017
    • Place of Presentation
      石川県金沢市 石川県政記念 しいのき迎賓館
    • Year and Date
      2017-03-03
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] いくつかの関数空間上のFourier multiplier等の作用素について2016

    • Author(s)
      佐藤圓治
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 関数空間上の作用素について2014

    • Author(s)
      佐藤圓治
    • Organizer
      調和解析セミナー2014
    • Place of Presentation
      ヒルズサンピア山形
    • Year and Date
      2014-12-25 – 2014-12-27
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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