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Research on Fourier integrals of several variables

Research Project

Project/Area Number 09640168
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionKanazawa University

Principal Investigator

SATO Shuichi  Kanazawa Univ., Faculty of Education, associate professor, 教育学部, 助教授 (20162430)

Co-Investigator(Kenkyū-buntansha) TOHGE Kazuya  Kanazawa Univ., Faculty of Faculty of Engineering, associate professor, 工学部, 助教授 (30260558)
KANJIN Yuichi  Kanazawa Univ., Faculty of Faculty of Engineering, professor, 工学部, 教授 (50091674)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1997: ¥800,000 (Direct Cost: ¥800,000)
KeywordsRough operators / Square functions / Littlewood-Paley theory / Hardy's inequality / Nevanlinna theory / meromorphic function
Research Abstract

(1)We proved the pointwise relations between some multiparameter square functions on R^n, and we applied them to prove H^p - L^p and L(log L)^<n-1> - L^<1, *> estimates for multiparameter Marcinkiewicz integrals. To show the weak type estimate, we also proved a resonance theorem on Orlicz spaces.
(2)We proved that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on L^p_ 1 <p < *, w * A_p (the weights of Muckenhoupt). The kernels are satisfying only size and cancellation conditions. Then, we gave some applications to the Carleson measures on the upper half space.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] Shuichi Sato: "Multiparameter Marcinkiewicz integrals and a resonance theorem" Bull.Fac.Ed.Kanazawa Univ. Natur. Sci. 48. 1-21 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shuichi Sato: "Remarks on square functions in the Littlewood-Paley theory" Bull.Austral.Math.Soc.85. 199-211 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Kanjin: "On Hardy type inequalities and Hankel transtorms" Monatsh.Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Sato: "Remarks on square functions in the Littlewood-Paley theory" Bull.Austral.Math.Soc.58. 199-211 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Sato: "Multiparameter Marcinkiewicz integrals and a resonance theorem" Bull.Fac.Ed.Kanazawa Univ.Natur.Sci.48. 1-21 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Kanjin: "On Hardy type inequalities and Hankel transforms" Monatsh.Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shuichi Sato: "Multiparameter Marcinkiewicz integrals and a resonance theorem" Bull:Fac.Ed.Kanazawa Univ.Natur.Sci.48. 1-21 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shuichi Sato: "Remarks on square functions in the Littlewood-Paley theory" Bull.Austral.Math.Soc.58. 199-211 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Kanjin: "On Hardy type inequalities and Hankol transforms" Monatsh.Math.

    • Related Report
      1998 Annual Research Report
  • [Publications] Shuichi Sato: "Some weighted weak type estimates for rough operators" Math.Nachr.187. 211-240 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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