Abstract and Applied Analysis

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

Farman Mamedov and Yusuf Zeren

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Abstract

The variable exponent Hardy inequality x β ( x ) - 1 0 x f ( t ) d t L p ( . ) ( 0 , l ) C x β ( x ) f L p ( . ) ( 0 , l ) , f 0 is proved assuming that the exponents p : ( 0 , l ) ( 1 , ) , β : ( 0 , l ) not rapidly oscilate near origin and 1 / p ( 0 ) - β > 0 . The main result is a necessary and sufficient condition on p , β generalizing known results on this inequality.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 342910, 7 pages.

Dates
First available in Project Euclid: 7 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412687017

Digital Object Identifier
doi:10.1155/2014/342910

Mathematical Reviews number (MathSciNet)
MR3208529

Zentralblatt MATH identifier
07022194

Citation

Mamedov, Farman; Zeren, Yusuf. A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 342910, 7 pages. doi:10.1155/2014/342910. https://projecteuclid.org/euclid.aaa/1412687017


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