Estimates for norms of two-weighted summation operators on trees for 1<p<q<∞1<p<q<\infty

In this paper, estimates for norms of weighted summation operators (discrete Hardy-type operators) on a tree are obtained for $1<p<q<\infty$ and for arbitrary weights and trees

An embedding theorem for weighted Sobolev classes on a John domain: case of weights that are functions of a distance to a certain h-set

Let $\Omega$ be a John domain, and let $\Gamma\subset \partial \Omega$ be an $h$-set. For some functions $h$ and some weight functions depending on distance from $\Gamma$, embedding theorems for a weighted Sobolev class is obtained

Estimates for norms of two-weighted summation operators on a tree under some conditions on weights

Two-side estimates for two-weighted discrete Hardy-type operators on a tree are obtained. For general weights we prove the discrete analogue of Evans - Harris - Pick theorem (it is a quite simple consequence from their result). It gives the order estimate for the norm of the weighted summation operator, but this estimate is rather complicated. Under some conditions on weights, we obtain estimates which are more simple and convenient for applications

Widths of weighted Sobolev classes with weights that are functions of distance to some h-set: some limiting cases

Here we obtain order estimates for widths of weighted Sobolev classes in the weighted Lebesgue space where parameters of the second weight satisfy some limiting conditions

Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin

In this paper we obtain asymptotic estimates of Kolmogorov and linear widths of the weighted Besov classes with singularity at the origin. In addition, estimates of Kolmogorov and linear widths of finite-dimensional balls in a mixed norm are obtained

Entropy numbers of embedding operators of weighted Sobolev spaces with weights that are functions of distance from some h-set

In this paper order estimates for entropy numbers of embeddings of weighted Sobolev spaces on a John domain are obtained. In addition, we obtain order estimates for entropy numbers of summation operators on trees

Estimates for entropy numbers of embedding operators of function spaces on sets with tree-like structure: some limiting cases

In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.Comment: arXiv admin note: text overlap with arXiv:1503.0014

Widths of weighted Sobolev classes on a domain with a peak: some limiting cases

Order estimates for Kolmogorov, Gelfand and linear widths of a weighted Sobolev class on a domain with a peak in a weighted Lebesgue space are obtained for some special weights

Widths of function classes on sets with tree-like structure

In this paper, estimates for Kolmogorov, Gelfand and linear widths of function classes on sets with a tree-like structure are obtained. As examples we consider weighted Sobolev classes on a John domain, as well as some function classes on a metric and combinatorial tree

Kolmogorov widths of the intersection of two finite-dimensional balls

In this paper we obtain order estimates for the Kolmogorov widths of the set $B_{p_0}^m\cap \nu B_{p_1}^m$ in $l_q^m$; here $0\le n\le m/2$, $p_0>p_1$, $q<\infty$