Interpolation and I¦-moment inequalities of noncommutative martingales

被引：33

作者：

Bekjan, Turdebek N. ^{[2
]}

Chen, Zeqian ^{[1
]}

机构：

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China

[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2012年 / 152卷 / 1-2期

关键词：

tau-Measurable operators; Noncommutative martingale; Interpolation; Phi-Moment martingale inequality; Noncommutative Orlicz space; KHINTCHINE INEQUALITIES; THEOREM; SPACES; EXTRAPOLATION;

D O I：

10.1007/s00440-010-0319-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is devoted to the study of phi-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative phi-moment analogues of martingale transformations, Stein's inequalities, Khintchine's inequalities for Rademacher's random variables, and Burkholder-Gundy's inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.

引用

页码：179 / 206

页数：28

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