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1998 Fiscal Year Final Research Report Summary

Study on harmonic analysis, partial differential equations and complex analysis

Research Project

Project/Area Number 08304009
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

ARAI Hitoshi  Tohoku University, Professor, 大学院・理学研究科, 教授 (10175953)

Co-Investigator(Kenkyū-buntansha) KURATA Kazuhiro  Tokyo Metropolitan University, Associate Professor, 理学部, 助教授 (10186489)
KURODA Shigetoshi  Gakushuin University, Professor, 理学部, 教授 (20011463)
KANJIN Yuichi  Kanazawa University, Professor, 工学部, 教授 (50091674)
MURATA Minoru  Tokyo Institute of Technology, Professor, 理学部, 教授 (50087079)
IGARI Satoru  Tohoku University, Professor, 大学院・理学研究科, 教授 (50004289)
Project Period (FY) 1996 – 1998
KeywordsSingular elliptic partial differential operators / Fourier multiplier / Parabolic equation / Hankel operators / Bloch functions / Toeplitz operator / Tangential Cauchy-Riemann equation / harmonic functions
Research Abstract

In this research project, we study harmonic analysis, partial differential equations, and complex analysis of several variables. We obtained results on the following topics : singular elliptic equations on Riemannian manifolds, pseudodifferential equations on stratified Lie groups, Bloch functions of several complex variables, Toeplitz operators, parabolic equations on Riemannian manifolds, tangential Cauchy-Riemann equations on strongly pseudoconvex CR manifolds, Hankel transforms, and some function spaces related to harmonic analysis. See the reference for details. We organized "Harmonic Analysis Seminar" (1996, 1997, 1998), and "Symposium on Harmonic Analysis, Partial Differential Equations, and Complex Analysis" (Jan. 1997, Jan. 1998). We printed and distributed the proceedings of these conferences to many Japanese researchers and institutions.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] 新井仁之: "実解析学の発展とその解析学への影響" 数学. 50.1. 29-55 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 新井仁之: "Bergman-Carleson measures and Bloch functions on strongly pseudaonuex domains" Reproducing Kernels and Their Applications. 印刷中.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 新井仁之: "Morrey Spaces and applications to hypoelliptic aguations on Cauchy-Riemaun manitolds" Aspects of Math : ″Algebm, Geanetry and Several Complex Variables″. 印刷中.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 村田實・石毛和宏: "An intrinsic metric approach to unigue neas of positive Cauclvy problem for parabolic equations" Math.2. 227. 313-335 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 勘甚裕一: "on Hardy type inequalities and Hankel toansfooms" Monatsh. Math.印刷中.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 倉田和浩: "On doubling property for non-negative weak solutions of elliptic and Parabolic PDE" Israel J.Math.印刷中.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 新井仁之: "フーリエ解析と関数解析学" 培風館 近刊,

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 村田實・倉田和浩: "偏微分方程式I" 岩波書店, 258 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hitoshi Arai: "The development of real analysis and its influence on analysis" Sugahu. 50・1 (Japanese). 29-55 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hitoshi Arai: "Bergman-Carleson measures and Bloch functions on strangly sendoconves domains" Reproducing Kernels and Their Appl. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hitoshi Arai: "Morney spaces and applications to hypoelliptic equations on Cauchy-Riemann manifolds" Aspects of Math : "Algelera, Geometry and Several Comple* Variables". (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Minoru Murata and K.Ishige: "An intrinsic metric approach to unique-ness of positive Cauchy problem for parabolic equations" Math Z.227. 313-335 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Kanjin: "On Houdy thpe inequalities and Hankel transforms" Monatsh.Math. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Kurata: "On doubling property for nonnegative weak solutions of elliptic and purobolic PDE" Israel J.Math. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hitoshi Arai: "Fourier Analysis and Functional Analysis" Baihukan. (to appear) (Book : Japanese).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Murata and K.Kurata: "Partial Differential Equations 1" Iwanami. 1997.

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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