齐次群上的哈代空间 Hardy Spaces on Homogeneous Groups

基本信息

Format：Paperback | 286 pages

Dimensions: 152 x 235 x 21.59mm | 397g

Publication date: 21 Jun 1982

Publisher：Princeton University Press

Imprint: Princeton University Press

ISBN: 9780691083100

页面参数仅供参考，具体以实物为准

内容简介

本专著的目的是对哈代空间（HP空间）的实变理论进行阐述。这一理论近年来引起了人们的极大关注，因为它使人们更好地理解了Rn中的相关课题，如奇异积分、乘数算子、Z大函数和一般的实变方法。由于其卓有成效的发展，现在希望对该理论的一些主要部分进行系统的阐述。除了这些阐述之外，这些笔记还包含了在更一般的环境下对该理论的重铸，其中底层Rn被一个同质群所取代。这一更广泛范围的理由来自两个方面。1）半简单李群和对称空间的理论，其中这种均质群作为 "边界 "自然出现，以及2）某些类别的非椭圆微分方程（特别是那些与几个复变数有关的方程），其中的模型情况发生在均质群上。近年来研究得Z广泛的例子是海森堡群的例子。

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

作者简介

Gerald Budge Folland是美国数学家，华盛顿大学的数学教授。他是几本数学分析教科书的作者。他的兴趣领域包括谐波分析（关于欧几里得空间和李群）、微分方程和数学物理学。他在普林斯顿大学的博士论文（1971年）的题目是 "球面上的切向考奇-里曼复合体"。

Gerald Budge Folland is an American mathematician and a professor of mathematics at the University of Washington. He is the author of several textbooks on mathematical analysis. His areas of interest include harmonic analysis (on both Euclidean space and Lie groups), differential equations, and mathematical physics. The title of his doctoral dissertation at Princeton University (1971) is "The Tangential Cauchy-Riemann Complex on Spheres".