Widths of embeddings in weighted function spaces

Details Widths of embeddings in weighted function spaces Widths of embeddings in weighted function spaces

2011-02-03

arxiv.org/abs/1102.0681v2

Mathematics

Functional Analysis

20 pages, 4 sections

Scientific paper

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.

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