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

TL;DR

This paper derives order estimates for the widths of weighted Sobolev classes in weighted Lebesgue spaces, focusing on cases where the weights depend on the distance to an h-set and satisfy certain limiting conditions.

Contribution

It provides new order estimates for widths of weighted Sobolev classes with weights related to h-sets under limiting parameter conditions.

Findings

Order estimates for widths derived

Results applicable to weights depending on distance to h-sets

Addresses limiting cases of weight parameters

Abstract

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.