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arXiv · 1212.1695

On a weighted variable spaces $L_{p(x), \omega}$ for $0< p(x)< 1$ and weighted Hardy inequality

Rovshan A. Bandaliev
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Abstract

In this paper a weighted variable exponent Lebesgue spaces $L_{p(x), \omega}$ for $0< p(x)< 1$ is investigated. We show that this spaces is a quasi-Banach spaces. Note that embedding theorem between weight variable Lebesgue spaces is proved. In particular, we show that $L_{p(x), \omega}(\Omega)$ for $0< p(x)< 1$ isn't locally convex. Also, in this paper a some two-weight estimates for Hardy operator are proved.

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Rovshan A. Bandaliev. 2012-12-07. On a weighted variable spaces $L_{p(x), \omega}$ for $0< p(x)< 1$ and weighted Hardy inequality. https://arxiv.org/abs/1212.1695

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