Widths of embeddings in weighted function spaces

TL;DR

This paper investigates the asymptotic behavior of various widths of compact embeddings between weighted Besov and Triebel-Lizorkin spaces, providing exact estimates and sharp bounds in broad settings.

Contribution

It offers new precise asymptotic estimates for approximation, Gelfand, and Kolmogorov numbers in weighted function space embeddings, including nonlimiting and polynomial weight cases.

Findings

Exact asymptotic estimates for widths in weighted embeddings

Sharp bounds for polynomial weights with small perturbations

Results applicable in quasi-Banach and nonlimiting scenarios

Abstract

We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain the exact estimates in almost all nonlimiting situations where the quasi-Banach setting is included. At the end we present complete results on related widths for polynomial weights with small perturbations, in particular the sharp estimates in the case $\alpha=d(\frac 1{p_2}-\frac 1{p_1})>0$ therein.