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Research on Fourier integrals and singular integrals

Research Project

Project/Area Number 20K03651
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 InstitutionKanazawa University

Principal Investigator

SATO Shuichi  金沢大学, 人間社会研究域, 客員研究員 (20162430)

Project Period (FY) 2020-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
KeywordsFourier series / singular integrals / square functions / square function / singular integral / Sobolev space / 調和解析 / Fourier 解析
Outline of Research at the Start

ユークリッド空間, 多様体, べき零Lie 群(特にhomogeneous group(斉次群))及びそれらの空間の直積空間における特異積分,擬微分作用素,固有関数展開のRiesz 平均,Ces`aro 平均等に関する種々の関数空間(Lebesgue 空間, Hardy 空間, Sobolev 空間等) 上での写像性,有界性(強有界性, 弱有界性) 等にかかわる調和解析の研究.

Outline of Final Research Achievements

The weighted Sobolev spaces with weights of the Muckenhoupt class are characterized by the square functions of Marcinkiewicz type defined by repeated averaging operations over balls or spheres. We considered some maximal singular integral operators with variable kernels on Rn with doubling measures and proved Lp and weak type estimates for them under certain sharp conditions. A survey on k-plane transforms are completed.

Academic Significance and Societal Importance of the Research Achievements

n 次元 Euclid 空間のボール上の平均により構成された Littlewood-Paley(L-P)関数によりSobolev 空間の特徴づけが証明された。このようなL-P関数は, 次数の高い Sobolev 空間に対しては平均をとる作用を次数に関係して繰り返すことにより定義される。これは通常の Euclid ノルム, dilation に対して考えられる Sobolev 空間に対しても新しい結果でる。この結果に類似のSobolev 空間の特徴づけがn 次元 Euclid 空間の球面上の平均により構成された L-P関数により証明された。

Report

(4 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (7 results)

All 2022 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 1 results) Remarks (3 results)

  • [Journal Article] Sobolev spaces and functions of Marcinkiewicz type with repeated averaging operations over spheres2022

    • Author(s)
      Shuichi Sato
    • Journal Title

      Partial Differential Equations and Applications

      Volume: 3 Issue: 5

    • DOI

      10.1007/s42985-022-00203-1

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev spaces with non-isotropic dilations and square functions of Marcinkiewicz type2022

    • Author(s)
      Sato Shuichi
    • Journal Title

      Studia Mathematica

      Volume: 267 Issue: 3 Pages: 295-320

    • DOI

      10.4064/sm210819-19-3

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Results in estimates for k-plane transforms2022

    • Author(s)
      Sato Shuichi、佐藤 秀一
    • Journal Title

      Surveys in Mathematics and its Applications

      Volume: 17 Pages: 29-78

    • DOI

      10.24517/00065941

    • ISSN
      1843-7265
    • URL

      http://hdl.handle.net/2297/00065941

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some weak type estimates for maximal singular integrals2022

    • Author(s)
      Shuichi Sato
    • Journal Title

      MATHEMATICAL INEQUALITIES and APPLICATIONS

      Volume: 25 Issue: 1 Pages: 221-249

    • DOI

      10.7153/mia-2022-25-14

    • NAID

      120007185655

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Remarks] researchmap

    • URL

      https://researchmap.jp/read0102999

    • Related Report
      2022 Annual Research Report 2021 Research-status Report
  • [Remarks] 金沢大学学術情報リポジトリKURA

    • Related Report
      2021 Research-status Report
  • [Remarks] 佐藤 秀一 (Shuichi Sato) - マイポータル - researchmap

    • URL

      https://researchmap.jp/read0102999

    • Related Report
      2020 Research-status Report

URL: 

Published: 2020-04-28   Modified: 2024-01-30  

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