Widths of embeddings in weighted function spaces

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.

20 pages, 4 sections

References in corpus (2)

• The Gelfand widths of ${\ell }_p$-balls for $0<p\le 1$
• Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces

Cited by in corpus (2)

• Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II
• Widths of embeddings of 2-microlocal Besov spaces