关于Hermite展开和Laguerre展开的Hardy-Littlewood型定理和系数乘子

On Hardy-Littlewood type theorems and coefficient multipliers for Hermite and Laguerre expansions

本文给出关于Hermite展开和Laguerre展开的系数乘子理论的研究进展的综合评述,主要侧重于本文作者在近期关于这一课题取得的成果,内容包括:关于Hermite展开的Hardy不等式的研究背景和解决过程,关于广义Hermite展开的Hardy-Littlewood型定理,Hardy空间中的函数关于广义Hermite展开和多元Hermite展开的各种系数乘子定理和Paley型不等式,Hardy空间中的函数关于Laguerre展开的系数乘子定理等.

This paper surveys the recent advances of the theory of coefficient multipliers associated with Hermite and Laguerre expansions, with an emphasis on the results of the authors on the topic. It includes, the background and the solution of the Hardy inequality associated with Hermite expansions, the Hardy-Littlewood type theorems associated with generalized Hermite expansions, several theorems about coefficient multipliers and the Paley type inequalities of functions in Hardy spaces associated with generalized Hermite expansions and multiple Hermite expansions, and the theorems about coefficient multipliers of functions in Hardy spaces associated with Laguerre expansions.