Full length article: Widths of embeddings in weighted function spaces

Authors:
Shun Zhang;Gensun Fang
Affiliations:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China and School of Computer Science and Technology, Anhui University, Hefei 230601, Anhui, China;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Venue:
Journal of Approximation Theory
Year:
2013

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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 @a=d(1p"2-1p"1)0 therein.