Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces

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.Comment: 18 pages, 4 sections, publishe

Widths of embeddings in weighted function spaces

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.Comment: 20 pages, 4 section