arXiv subjects
Publications and source records attributed to Dmitrii V. Prokhorov.
Characterizations of the associated spaces and second associated spaces of the Hardy space on $\mathbb{R}^n$ are given. Some results on the associated spaces of the $\textrm{BMO}(\mathbb{R}^n)$ space are proved also.
We study weigted altered Cesàro space Ch$_{\infty,w}(I)$, which is non-ideal enlargement of the usual Cesàro space. We prove the connection of the space with one weighted Sobolev space of first order on real line and give characterization of associate spaces for the space.
We study weighted altered Cesàro and Copson spaces, which is non-ideal enlargement of the usual spaces. We give full characterization of dual spaces for the spaces.
Weighted $L^p-L^r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the Lorentz $Γ-$spaces is given.