中文摘要：

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.

英文摘要：

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.