Weak norm inequalities for martingales and geometry of Banach spaces

被引：5

作者：

Osekowski, Adam ^{[1
]}

机构：

[1] Univ Warsaw, Dept Math Informat & Mech, PL-02097 Warsaw, Poland

来源：

STATISTICS & PROBABILITY LETTERS | 2012年 / 82卷 / 03期

关键词：

Martingale; Martingale transform; Differential subordination; UMD space;

D O I：

10.1016/j.spl.2011.12.007

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：

Let f, g be two Hilbert-space-valued martingales such that g is differentially subordinate to f. The paper contains the proof of the estimate ||g||(p,infinity) <= 2p(p + n)/p - 1 ||f||(p,infinity), 1 < p < infinity. The constant is shown to be of optimal order for p --> infinity and for p --> 1. Related results for transforms of UMD-valued martingales are also established. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：411 / 418

页数：8

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