双指标非交换鞅的收敛性和不等式  

CONVERGENCE AND INEQUALITIES OF TWO-PARAMETER NONCOMMUTATIVE MARTINGALES

作　　者：曹芳[1] 侯友良[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2015年第6期1511-1520,共10页Journal of Mathematics

基　　金：国家自然科学基金资助(11271293)

摘　　要：本文研究了双指标非交换鞅的收敛性和不等式问题.利用非交换代数和单指标鞅的方法,获得了双指标Lp-有界鞅(1≤p≤∞)的收敛性,L1-收敛性和一致可积的关系;推广了双指标非交换鞅的两个不等式,即Burkholder-Gundy不等式和强鞅的Davis不等式.In this paper,we discuss the convergence and inequalities of two-parameter noncommutative martingales.By using noncommutative algebra and one-paremeter martingales methods,we have the convergence of Lp-bounded martingales（1 ≤ p ≤ ∞）,the relation between L1-convergence and uniformly integrability of Lp-bounded martingales.And we generalize two inequalities of two-parameter noncommutative martingales,i.e.,Burkholder-Gundy inequality and Davis＇ s inequality for strong martingales.

关 键 词：von NEUMANN代数 双指标鞅 Burkholder-Gundy不等式 Davis不等式 强鞅 

分 类 号：O177.5[理学—数学]