权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Weight theory related to harmonic analysis on groups -in harmony with representation theory

与群调和分析相关的权重理论——与表示论一致

基本信息

批准号：
13640190
负责人：
KAWAZOE Takeshi
金额：
$ 2.18万
依托单位：
Keio University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

In this research we investigated the usage of fractional integrals in real analysis and also in harmonic analysis on semisimple Lie groups. E. Nakai, the investigator, studied boundedness of the fractional integral operators on various function spaces, especially, he generalized the operators and function spaces. T. Kawazoe, the head investigator, applied the theory of fractional integrals to construct real Hardy spaces on semisimple Lie groups. In this sense, we attained our aim of this research -in harmony with representation theory and real analysis.The theory of real Hardy spaces was generalized on the so-called space of homogeneous type satisfying the doubling condition, however, little works were done on the space of non-homogeneous type. In this research we took real rank one semisimple Lie groups G as an example of the space of non-homogeneous type, and introduced real Hardy spaces for K-bi-invariant functions. This corresponds to harmonic analysis on Fourier-Jaccobi transforms … More and on the weight theory with exponential growth order. We first, by using the Abel transform, reduced the Fourier-Jaccobi analysis to Euclidean one on the real line R. Since the Abel transform was written by fractional integrals, the method of real analysis related to fractional integrals were useful in this analysis. Next, five extended the theory of fractional integrals and derivatives and then characterized real Hardy spaces defined by maximal functions and atoms. Our main theorem is the following. Let W be the modified Abel transform with Exp(ρx)-multiplication and V the inverse of W. Then, we see H1 (G//K) ⊂V (H1(R)), where H1(G//K) and HI(R) are respectively the real Hardy spaces on G and R defined by the radial maximal functions. Moreover, let A1(G//K)+ denote the atomic Hardy space on G defined by restricting the moment condition of atoms only for ones with redius <1. Then it follows that H1(G//K)= V(H1(R))∩A1(G//K)+. In the proof we applied some methods in real analysis related to fractional integrals and atomic decompositions. Less

在这项研究中，我们研究了使用分数次积分在真实的分析，也在调和分析半单李群。E. Nakai研究了分数次积分算子在各种函数空间上的有界性，特别是推广了分数次积分算子和函数空间。T.首席研究员川佐江运用分数次积分理论在半单李群上构造了真实的哈代空间。在这个意义上，我们达到了我们的研究目的--与表示论和真实的分析相协调，将真实的哈代空间的理论推广到了所谓的满足加倍条件的齐型空间上，而在非齐型空间上的工作还很少。本文以真实的秩一的半单李群G为例，引入了K-双不变函数的真实的哈代空间。这对应于Fourier-Jacobi变换的谐波分析 ...更多信息以及指数增长阶的权理论。我们首先利用Abel变换将Fourier-Jaccobi分析化为真实的直线R上的欧氏分析。由于Abel变换是用分数次积分来表示的，因此与分数次积分相关的真实的分析方法在这一分析中是有用的。其次，Five推广了分数阶积分和导数的理论，并刻画了由极大函数和原子定义的真实的哈代空间。我们的主要定理如下。设W是带Exp（ρx）-乘法的修正Abel变换，V是W的逆.然后，我们得到H 1（G//K）≠ V（H 1（R）），其中H 1（G//K）和H 1（R）分别是由径向极大函数定义的G和R上的真实的哈代空间.此外，设A 1（G//K）+表示G上的原子哈代空间，该空间是通过限制原子的矩条件而定义的.因此，H1（G//K）= V（H1（R））<$A1（G//K）+。在证明中，我们应用了真实的分析中与分数次积分和原子分解有关的一些方法。少