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

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  • Farman Mamedov
  • Yusuf Zeren

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:342910
DOI: 10.1155/2014/342910
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