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Kühn, Thomas; Leopold, Hans-Gerd; Sickel, Winfried; Skrzypczak, Leszek

Entropy numbers of Sobolev embeddings of radial Besov spaces. (English) Zbl 1047.47016

J. Approximation Theory 121, No. 2, 244-268 (2003).
This paper investigates the quality of compact embedding between the radial subspaces of Besov and Triebel-Lizorkin spaces on the Euclidean \(n\)-space \(\mathbb{R}^n\). In particular, with proper definitions, the entropy numbers of Sobolev embeddings of radial Besov spaces are independent of the difference \(s_0-s_1\) as long as the embedding is compact.
Reviewer: Joe Howard (Portales/New Mexico)

Cited in 11 Documents

MSC:

47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47B38 Linear operators on function spaces (general)

Keywords:

radial spaces; weighted spaces; atomic decompositions; entropy numbers; traces; compact embeddings
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References:

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