arXiv subjects

Rovshan A. Bandaliev

Publications and source records attributed to Rovshan A. Bandaliev.

3 recordsLinked to original sources

arXiv2013

Corrections to the paper "The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces"

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space. Note that the proof of multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent don't contained any mistakes. But at the proving of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in this paper. This result is assigned as Theorem 5 in noted paper. In other words, sufficient conditions for general weights ensuring the validity of the two-weight strong type inequalities for some sublinear operator was found. In this theorem the inequality (9) isn't true. In this note we give the details of the correct argument. We presume that the reader is familiar with the contents and notation of our original paper. At the heart of our correction is the following Theorem which replaces Theorem 5.

math.CA↗

arXiv2012

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

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

math.CA↗

arXiv2012

On a two-weight criteria for multidimensional Hardy type operator in $p$-convex Banach function spaces and some application

The main goal of this paper is to prove a two-weight criteria for multidimensio-nal Hardy type operator from weighted Lebesgue spaces into $p$-convex weighted Banach function spaces. Analogously problem for the dual operator is considered. As application we prove a two-weight criteria for boundedness of multidimensional geometric mean operator and sufficient condition on the weights for boundedness of certain sublinear operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spaces.

math.FA↗