Studies of Harmonic Analysis

谐波分析研究

• 批准号: 60460003
• 负责人: IGARI Satoru
• 金额: $ 4.16万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-60460003/
• 关键词: Harmonic function; subharmonic function; Hardy space; Operator algebra; Evolution equation; Semi-simple group; D-module; 補間定理

Classical harmonic analysis has been a considerable flowering duaring the past 15 years starting from the results due to Fefferman-Stein,Carleson and others. The object of our program was to study the idea of classical harmonic analysis and to develop it in various fields in mathematics by the coorperative research with several specialists in our institute.An extract of our results is the following :1. An interpolation theorem of operators on a product measure space is shown. As applications we solved partially a problem on Riesz-Bochner means and on Kakeya's maximal function. Hardy spaces on a product space are investigated with connection to holomorphic functions of two variables.We are now generalizing classical Hardy space theory to a manifold of negative curvature.2. We have studied non-linear evolution equations getting several results on a property of the solutions of Navier-Stokes equation near t = 0, existence of global solutions and analiticity of solutions.3. By a method of D-modules it is succeeded to analyse and classify the singularities of characters through Harish-Chandra's differential equation. We have a program to develop these researches in future.

经典调和分析从Fefferman-Stein，Carleson等人的结果开始，在过去的15年里得到了相当大的发展。本程序的目的是研究经典调和分析的思想，并通过与我所几位专家的合作研究，将其推广到数学的各个领域。我们的结果摘录如下：1.证明了乘积测度空间上的算子的一个内插定理。作为应用，我们部分地解决了Riesz-Bochner平均和Kakeya极大函数的一个问题。研究乘积空间上的Hardy空间与两个变量的全纯函数的关系。我们现在将经典的Hardy空间理论推广到负曲率流形上。研究了非线性发展方程，得到了关于Navier-Stokes方程在t=0附近解的一个性质、整体解的存在性和解的无理性的几个结果。利用D-模的方法，利用Harish-Chandra方程对特征的奇异性进行了分析和分类。我们有一个在未来开展这些研究的计划。

项目成果

HOTTA,Ryoshi: "Introduction to D-Modules" Institute of Mathematical Sciences,Madras, (1986)

HOTTA,Ryoshi：“D 模块简介”，马德拉斯数学科学研究所，（1986 年）

IGARI,Satoru: "Interpolation of linear operators in Lebesgue spaces with mixed norm and its applications to Fourier analysis" Tohoku Mathematical Journal. 38. 469-490 (1986)

IGARI，Satoru：“具有混合范数的勒贝格空间中线性算子的插值及其在傅里叶分析中的应用”东北数学杂志。

HOTTA, Ryoshi: Institute of Mathematical Sciences, Madras. Introduction to D-Modules, (1986)

HOTTA, Ryoshi：数学科学研究所，马德拉斯。

IGARI Satoru: Tohoku Math.J.38. 469-490 (1986)

IGARI 悟：东北数学.J.38。

HOTTA Ryoshi: Advances Studies in Pure Math.6. 127-138 (1985)

HOTTA Ryoshi：纯数学的进展.6。