Weighted Hardy modular inequalities in variable Lp spaces for decreasing functions

被引：20

作者：

Boza, Santiago ^{[1
]}

Soria, Javier ^{[2
]}

机构：

[1] Univ Politecn Cataluna, Dept Appl Math 4, EPSEVG, E-08880 Vilanova I La Geltru, Spain

[2] Univ Barcelona, Dept Appl Math & Anal, E-08007 Barcelona, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 348卷 / 01期

关键词：

modular inequalities; hardy operator; B-p weights; variable L-p spaces; monotone functions;

D O I：

10.1016/j.jmaa.2008.07.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study weighted modular inequalities with variable exponents for the Hardy operator restricted to non-increasing functions. We show that the exponents p(.) for which these modular inequalities hold must have a constant oscillation at zero, which implies that these exponents are either constant or extremely oscillating near the origin. Similarly to the constant case, we introduce the class of weights B-p(.), and prove some of the classical properties in this context. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：383 / 388

页数：6