On weighted weak type maximal inequalities for martingales

被引：8

作者：

Kikuchi, M ^{[1
]}

机构：

[1] Toyama Univ, Dept Math, Toyama 9308555, Japan

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2003年 / 6卷 / 01期

关键词：

weak type inequality; martingale; weight; Young function;

D O I：

10.7153/mia-06-16

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Phi be a Young function and (u, v) a pair of weights on a probability space. We consider the inequality sup Phi(lambda) E[ u :{Mf > lambda}] less than or equal to E[Phi (C\.f(infinity)\) v] lambda is an element of (0,infinity) for martingales f = (f(n))(nis an element ofZ+) , where Mf = sup(nis an element ofZ+) \fn\ and f(infinity) = lim(n) f(n) a.s. We give some necessary and sufficient conditions for this inequality to hold, and extend Uchiyama's result.

引用

页码：163 / 175

页数：13