Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II

Abstract

We consider the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. Our main purpose here is to complement our previous results in \cite{ZF10} in the context of the quasi-Banach setting, $0<p,q\le \infty$. In addition, sharp estimates for their approximation numbers in several cases left open in Skrzypczak (JAT, 2005) are provided.

16 pages, essentially the same contribution as arXiv:1102.0677v1 but with improved results and a section about comparisons with approximation numbers

References in corpus (4)

• The Gelfand widths of ${\ell }_p$-balls for $0<p\le 1$
• Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces
• s-Numbers of compact embeddings of function spaces on quasi-bounded domains
• Widths of embeddings in weighted function spaces

Cited by in corpus (2)

• Weyl Numbers of Embeddings of Tensor Product Besov Spaces
• Widths of embeddings of 2-microlocal Besov spaces