A Necessary and Sufficient Condition for Hardy's Operator in the Variable Lebesgue Space

被引：4

作者：

Mamedov, Farman ^{[1
,2
]}

Zeren, Yusuf ^{[3
]}

机构：

[1] SOCAR Co, Inst Math & Mech, NAS, Baku 1141, Azerbaijan

[2] SOCAR Co, OGRDI, Baku 1141, Azerbaijan

[3] Yildiz Tech Univ, Dept Math, TR-34220 Davutpasha, Turkey

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

关键词：

WEIGHTED INEQUALITY; REGULARITY;

D O I：

10.1155/2014/342910

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The variable exponent Hardy inequality parallel to x(beta(x)-1) integral(x)(0) f(t)dt parallel to(LP(.)(0,l)) <= C parallel to x(beta(x)) f parallel to(LP(.)(0,l)), f >= 0 is proved assuming that the exponents p : (0,l) -> (1, infinity), beta : (0, l) -> R not rapidly oscilate near origin and 1/p'(0) - beta > 0. The main result is a necessary and sufficient condition on p, beta generalizing known results on this inequality.

引用

页数：7

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