论文标题
对HERMITE扩展的非共同分析
Noncommutative analysis of Hermite expansions
论文作者
论文摘要
本文致力于研究对非交换性$ l_ {p} $ - 空格作用的HERMITE操作员。在第一部分中，我们建立了与HERMITE运算符相关的Bochner-Riesz手段的非交通性最大不平等，然后获得相应的点收敛定理。特别是，我们开发了Bochner-Riesz对Hermite运营商的bochner-riesz含义的非交流性stein \ textquoteright的定理。本文的第二部分介绍了Hermite运营商的两个乘数定理。我们对这部分的分析是基于与Hermite扩展相关的古典Littlewood-Paley-Stein理论的非共同类似物。
This paper is devoted to the study of Hermite operators acting on noncommutative $L_{p}$-spaces. In the first part, we establish the noncommutative maximal inequalities for Bochner-Riesz means associated with Hermite operators and then obtain the corresponding pointwise convergence theorems. In particular, we develop a noncommutative Stein\textquoteright s theorem of Bochner-Riesz means for the Hermite operators. The second part of this paper deals with two multiplier theorems for Hermite operators. Our analysis on this part is based on a noncommutative analogue of the classical Littlewood-Paley-Stein theory associated with Hermite expansions.
