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Research on Fourier integrals and singular interals

Research Project

Project/Area Number 16K05195
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Sato Shuichi  金沢大学, 学校教育系, 教授 (20162430)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywordssingular integrals / square functions / Hardy spaces / Sobolev spaces / Littlewood-Paley 関数 / Hardy 空間 / Littlewood-Paley / Littlewood-Paley / Sobolev space / Hardy space / homogeneous group / Marcinkiewicz function / Sobolev space / Hardy space / Fourier series
Outline of Final Research Achievements

We considered singular integrals on homogeneous groups including Heisenberg groups and established weak type estimates on the weighted Lebesgue spaces. The kernel of the singular integral is assumed to have no regularity and only a size condition and cancelation were assumed. Characterizations of Hardy spaces on homogeneous groups and some Sobolev spaces were obtained in terms of Littlewood-Paley functions and Lusin area integrals.

Academic Significance and Societal Importance of the Research Achievements

ある種の特異積分作用素を考えて, その荷重 Lebesgue 空間上での弱有界性が示された. ここで, 特異積分作用素には滑らかさの正則性が仮定されていなく, サイズに関する最小の仮定と cancellation に関する仮定が置かれているのみである. Littlewood-Paley 関数, Lusinの面積積分により斉次群上のHardy 空間の特徴づけ, ある種のSobolev 空間の特徴づけが得られた.

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (9 results)

All 2019 2018 2017 2016

All Journal Article (9 results) (of which Peer Reviewed: 9 results,  Acknowledgement Compliant: 3 results)

  • [Journal Article] Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity2019

    • Author(s)
      Shuichi Sato
    • Journal Title

      MATHEMATICA SCANDINAVICA

      Volume: 125 Issue: 1 Pages: 135-162

    • DOI

      10.7146/math.scand.a-114725

    • NAID

      120006764683

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness of Littlewood-Paley operators relative to non-isotropic dilations2019

    • Author(s)
      Shuichi Sato
    • Journal Title

      Czech Math J

      Volume: 69 Issue: 2 Pages: 337-351

    • DOI

      10.21136/cmj.2018.0313-17

    • NAID

      120006518034

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Vector valued inequalities and Littlewood-Paley operators on Hardy spaces2019

    • Author(s)
      Shuichi Sato
    • Journal Title

      Hokkaido Math.

      Volume: 48 Issue: 1 Pages: 61-84

    • DOI

      10.14492/hokmj/1550480644

    • NAID

      120006766229

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterization of parabolic Hardy spaces by Littlewood-Paley functions2018

    • Author(s)
      Shuichi Sato
    • Journal Title

      Results Math

      Volume: 73 Issue: 3 Pages: 106-106

    • DOI

      10.1007/s00025-018-0867-9

    • NAID

      120006764681

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized Littlewood-Paley characterizations of fractional Sobolev spaces2018

    • Author(s)
      Shuichi Sato, Fan Wang., Dachun Yang and Wen Yuan
    • Journal Title

      Communications in Contemporary Mathematics

      Volume: 20 Issue: 07 Pages: 1750077-1750077

    • DOI

      10.1142/s0219199717500778

    • NAID

      120006532178

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spherical square functions of Marcinkiewicz type with Riesz potentials2017

    • Author(s)
      Shuichi Sato
    • Journal Title

      Arch. Math.

      Volume: 108

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Littlewood-Paley equivalence and homogeneous Fourier multipliers2017

    • Author(s)
      Shuichi Sato
    • Journal Title

      Integr. Equ. Oper. Theory

      Volume: 87

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Square functions related to integral of Marcinkiewicz and Sobolev spaces2016

    • Author(s)
      Shuichi Sato
    • Journal Title

      Linear and Nonlinear Analysis

      Volume: 2

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Weighted weak type (1,1) estimates for singular integrals with non-isotropic homogeneity2016

    • Author(s)
      Shuichi Sato
    • Journal Title

      Arkiv for Matematik

      Volume: 54

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant

URL: 

Published: 2016-04-21   Modified: 2021-02-19  

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