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Study of singular integrals and Triebel-Lizorkin spaces associated to surfaces

Research Project

Project/Area Number 15K04942
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

YABUTA KOZO  関西学院大学, 数理科学研究センター, 客員研究員 (30004435)

Co-Investigator(Kenkyū-buntansha) 北原 和明  関西学院大学, 理工学部, 教授 (40195277)
Co-Investigator(Renkei-kenkyūsha) SATO SHUUICHI  金沢大学, 人間社会研究域学校教育系, 教授 (20162430)
Research Collaborator DING Yong  北京師範大学, 数学科学学院, 教授
XUE Qingying  北京師範大学, 数学科学学院, 教授
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords調和解析 / フーリエ解析 / 実解析 / 函数解析 / 函数解析学 / 特異積分 / 実函数論
Outline of Final Research Achievements

For singular integrals with kernel associated to the surface of the form {x=Ψ(|y|)} etc, we obtained several good estimates in Triebel-Lizorkin spaces and Besov spaces. We published 14 results for singular integrals with rough kernel, vector space valued singular integrals, multilinear singular integrals, and maximal singular intefrals. These contribute to the development of the study of singular integrals.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (12 results)

All 2018 2017 2016 2015

All Journal Article (11 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 11 results,  Open Access: 6 results,  Acknowledgement Compliant: 4 results) Presentation (1 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] The Multilinear Littlewood-Paley Operators with Minimal Regularity Conditions2018

    • Author(s)
      Mingming CAO, Kozo YABUTA
    • Journal Title

      J Fourier Anal Appl

      Volume: Online Issue: 3 Pages: 45-45

    • DOI

      10.1007/s00041-018-9613-7

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On multilinear fractional strong maximal operator associated with rectangles and multple weights2017

    • Author(s)
      Kozo YABUTA, Mingming CAO, Qingying XUE
    • Journal Title

      Rev. Mat. Iberoam.

      Volume: 33 Issue: 2 Pages: 555-572

    • DOI

      10.4171/rmi/949

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Littlewood-Paley operators (Correction to 33 (2013), no. 3, 209-218)2017

    • Author(s)
      Kozo YABUTA
    • Journal Title

      Analysis (Berlin)

      Volume: 37 Issue: 4 Pages: 243-244

    • DOI

      10.1515/anly-2017-0044

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the bilinear square Fourier multiplier operators and related multilinear square functions2017

    • Author(s)
      Zengyan SI, Qingying XUE, Kozo YABUTA
    • Journal Title

      Sci. China Math.

      Volume: 60 Issue: 8 Pages: 1477-1502

    • DOI

      10.1007/s11425-016-0324-3

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Remark on the Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces2016

    • Author(s)
      Kozo YABUTA
    • Journal Title

      SCIENTIAE MATHEMATICAE JAPONICAE

      Volume: 79 Pages: 165-174

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces of revolution2016

    • Author(s)
      Yong DING and Kozo YABUTA
    • Journal Title

      Sci. China, Math.

      Volume: 59 Issue: 9 Pages: 1721-1736

    • DOI

      10.1007/s11425-016-5154-1

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Weighted estimates for fractional type Marcinkiewicz integral operators associated to surfaces2016

    • Author(s)
      Yoshiro SAWANO and Kozo YABUTA
    • Journal Title

      Advanced Lectures in Mathematics (ALM)

      Volume: 34 Pages: 331-367

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

    • Author(s)
      Shuichi SATO
    • Journal Title

      Ark. Mat.

      Volume: 54 Issue: 1 Pages: 157-180

    • DOI

      10.1007/s11512-015-0215-1

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces2015

    • Author(s)
      Kozo YABUTA
    • Journal Title

      Appl. Math. J. Chinese Univ. Ser. B

      Volume: 30 Issue: 4 Pages: 418-446

    • DOI

      10.1007/s11766-015-3358-8

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence and boundedness of multilinear Littlewood-Paley operators on Campanato spaces2015

    • Author(s)
      Sha HE, Qingying XUE, Ting MEI, Kozo YABUTA
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 432 Issue: 1 Pages: 86-102

    • DOI

      10.1016/j.jmaa.2015.06.037

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the theory of multilinear Littlewood–Paley <i>g</i>-function2015

    • Author(s)
      Qingying XUE, Xiuxiang PENG, Kozo YABUTA
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 67 Issue: 2 Pages: 535-559

    • DOI

      10.2969/jmsj/06720535

    • NAID

      130005069898

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Besov and Triebel-Lizorkin space estimates for fractional diffusion2016

    • Author(s)
      Kozo YABUTA
    • Organizer
      The International Conference on Harmonic Analysis and Applications
    • Place of Presentation
      Henan Polytechnic University, Jiaozuo (China)
    • Year and Date
      2016-05-20
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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