Study on harmonic analysis, partial differential equations and complex analysis

调和分析、偏微分方程和复分析研究

• 批准号: 08304009
• 负责人: ARAI Hitoshi
• 金额: $ 5.18万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304009/
• 关键词: Singular elliptic partial differential operators; Fourier multiplier; Parabolic equation; Hankel operators; Bloch functions; Toeplitz operator; Tangential Cauchy-Riemann equation; harmonic functions; 退化楕円型偏微分方程式; 接コーシー・リーマン方程式; 調和解析; CR多様体; マル

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.

在该研究项目中，我们研究了谐波分析，部分微分方程以及几个变量的复杂分析。 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 分析。有关详细信息，请参见参考。我们组织了“谐波分析研讨会”（1996，1997，1998）和“谐波分析，部分微分方程和复杂分析的研讨会”（1997年1月，1997年1月）。我们将这些会议的会议记录并分发给了许多日本研究人员和机构。

项目成果

倉田和浩: "On doubling property for non-negative weak solutions of elliptic and Parabolic PDE" Israel J.Math.印刷中.

Kazuhiro Kurata：“关于椭圆和抛物型偏微分方程非负弱解的加倍性质”Israel J.Math 正在出版。

M.Murata and K.Kurata: "Partial Differential Equations 1" Iwanami. 1997.

M.Murata 和 K.Kurata：“偏微分方程 1”Iwanami。

新井仁之: "フーリエ解析と関数解析学" 培風館 近刊,

新井仁：《傅里叶分析与泛函分析》百风馆即将出版，

勘甚裕一: "Hardy's inequalities for Hermite and Laguerre expansions" Bull.London Math.Soc.(発表予定).

Yuichi Kanjin：“哈代的埃尔米特和拉盖尔展开不等式”Bull.London Math.Soc。

Hitoshi Arai: "Morney spaces and applications to hypoelliptic equations on Cauchy-Riemann manifolds" Aspects of Math : "Algelera, Geometry and Several Comple* Variables". (in press).

Hitoshi Arai：“莫尼空间及其在柯西-黎曼流形上的亚椭圆方程中的应用”数学方面：“阿尔杰拉、几何和几个复杂*变量”。