论文标题
sobolev的空间在Gelfand对
Sobolev spaces on Gelfand pairs
论文作者
论文摘要
本文的主要目的是在Gelfand Pairs的背景下研究Sobolev空间。文章开始于为研究主题提供历史概述和动机，并摘要文献状态。接下来是对Gelfand对的谐波分析的一般概述，首先是通过球形函数和球形变换的阳性函数概念开始，并以Hausdorff-Young的不平等结论。本文的主要部分介绍了Gelfand Pairs上Sobolev空间的概念，并研究了这些空间的特性。事实证明，在这种广义的环境中，Sobolev嵌入定理和Rellich-Kondrachov定理仍然成立（如果考虑到某些技术警告的话）。
The primary aim of the paper is the study of Sobolev spaces in the context of Gelfand pairs. The article commences with providing a historical overview and motivation for the researched subject together with a summary of the current state of the literature. What follows is a general outline of harmonic analysis on Gelfand pairs, starting with a concept of positive-semidefinite functions, through spherical functions and spherical transform and concluding with the Hausdorff-Young inequality. The main part of the paper introduces the notion of Sobolev spaces on Gelfand pairs and studies the properties of these spaces. It turns out that Sobolev embedding theorems and Rellich-Kondrachov theorem still hold true in this generalized context (if certain technical caveats are taken into consideration).
