Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces

TL;DR

This paper investigates the asymptotic behavior of Gelfand and Kolmogorov numbers for Sobolev embeddings between weighted Besov and Triebel-Lizorkin spaces, providing sharp estimates in the non-limiting case.

Contribution

It offers new sharp asymptotic estimates for Gelfand and Kolmogorov numbers in the context of weighted Sobolev embeddings, extending previous results.

Findings

Sharp asymptotic estimates for Gelfand numbers

Sharp asymptotic estimates for Kolmogorov numbers

Results applicable to non-limiting cases

Abstract

In this paper we study the Gelfand and Kolmogorov numbers of Sobolev embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights. The sharp asymptotic estimates are determined in the so-called non-limiting case.