This article is cited in 10 papers

On Hardy-type inequalities in weighted variable exponent spaces $L_{p(x),\omega}$ for $0<p(x)<1$

R. A. Bandaliev

Department of mathematical analysis, Institute of mathematics and mechanics, National academy of sciences of Azerbaijan, 9 B. Vahabzade St., Az 1141 Baku

Abstract: In this paper two-weighted inequalities for the Hardy operator and its dual operator acting from one weighted variable Lebesgue space to another weighted variable Lebesgue space are proved. In particular, sufficient conditions on the weights ensuring the validity of two-weighted inequalities of Hardy type are found. Also an embedding theorem for weighted variable Lebesgue spaces is proved.

Keywords and phrases: the Hardy inequality, $L_{p(x),\omega}$-spaces with $0<p(x)<1$, weights, embeddings.

MSC: 47B38

Received: 14.04.2012

Language: English