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.
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页数：7
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