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

Farman Mamedov and Yusuf Zeren

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: The variable exponent Hardy inequality xβ(x)-1∫0x f(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l), f ≥ 0 is proved assuming that the exponents p : (0, l)→(1, ∞), β : (0, l) → ℝ 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.

Date: 2014
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https://doi.org/10.1155/2014/342910

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:342910

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