非交换Hp空间理论的若干进展——纪念李国平院士吴新谋教授诞辰100周年

摘要/Abstract

摘要：

该文分两部分综述非交换 H_p 空间理论的研究背景、发展线路以及某些最新进展. 第一部分介绍非交换Hardy 空间理论, 包括有限次对角代数的基本性质 (如唯一正规态开拓性质、分解性质、对数模性、不变子空间性质等), Szeg\"{o} 与Riesz 型分解定理和H¹-BMO 对偶定理等. 第二部分综述非交换
H_p鞅空间理论, 主要介绍各种非交换鞅不等式以及作者与合作者在非交换Hardy 鞅空间原子分解方面获得的最新结果. 该文还给出了非交换H_p空间理论有待解决的一些问题和潜在的发展方向.

关键词: von Neumann 代数, 非交换L_p空间, 非交换Hardy 空间, 非交换鞅

Abstract:

We give a survey on theory of noncommutative H_p spaces. These include noncommutative Szeg\"o and Riesz theorems, H¹-BMO duality, noncommutative Burkholder-Gundy martingale inequalitity, noncommutative Burkholder martingale inequality, atomic decomposition for Hardy spaces of noncommutative martingales and so on. We also mention some open problems in the fileds.

Key words: Von Neumann algebra, Noncommutative L_p space, Noncommutative Hardy space, Noncommutative martingale

中图分类号:

46L53

陈泽乾, 吐尔德别克. 非交换H_p空间理论的若干进展——纪念李国平院士吴新谋教授诞辰100周年[J]. 数学物理学报, 2010, 30(5): 1263-1275.

CHEN Ze-Qian, Turdebek N.Bekjan. Some Advances on Theory of Noncommutative H_p Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(5): 1263-1275.

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