Maximal Inequality Associated to Doubling Condition for State Preserving Actions

Panchugopal Bikram, Diptesh Saha
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Abstract

In this article, we prove maximal inequality and ergodic theorems for state preserving actions on von Neumann algebra by an amenable, locally compact, second countable group equipped with the metric satisfying the doubling condition. The key idea is to use Hardy-Littlewood maximal inequality, a version of the transference principle, and certain norm estimates of differences between ergodic averages and martingales.
与状态保持行动的加倍条件相关的最大不等式
在这篇文章中,我们证明了冯-诺依曼代数上的保态作用的最大不等式和遍历定理,这些保态作用是由一个可亲的、局部紧凑的、第二可数的、配备了满足加倍条件的度量的群来实现的。其关键思路是利用哈代-利特尔伍德最大不等式、转移原理的反演以及对遍历平均数与马氏数之间差异的某些规范估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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