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

2012/12/07 by Rovshan A‎. ‎Bandaliev, Bandaliev, Rovshan A.
Mathematics · Social Sciences · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Polish Law and Legal System #Polish Legal and Social Issues

paper · pdf · doi:10.48550/arxiv.1212.1695

openalex publication_date 2012/12/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper a weighted variable exponent Lebesgue spaces L_{p(x), ω} for 0&lt; p(x)&lt; 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), ω}(Ω) for 0&lt; p(x)&lt; 1 isn't locally convex. Also, in this paper a some two-weight estimates for Hardy operator are proved.

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