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!ENTROPY NUMBERS OF EMBEDDINGS OF WEIGHTED BESOV SPACES. II

Published online by Cambridge University Press:  30 May 2006

Thomas Kühn ,
Hans-Gerd Leopold ,
Winfried Sickel  and
Leszek Skrzypczak
Thomas Kühn
Affiliation:
Mathematisches Institut, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany (kuehn@math.uni-leipzig.de)
Hans-Gerd Leopold
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1-2, 07743 Jena, Germany (leopold@minet.uni-jena.de; sickel@minet.uni-jena.de)
Winfried Sickel
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 1-2, 07743 Jena, Germany (leopold@minet.uni-jena.de; sickel@minet.uni-jena.de)
Leszek Skrzypczak
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, Pl-61-614 Poznan, Poland (lskrzyp@amu.edu.pl)
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Abstract

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We investigate the asymptotic behaviour of the entropy numbers of the compact embedding $B^{s_1}_{p_1,q_1}(\mathbb{R}^d,w_1)\hookrightarrow B^{s_2}_{p_2,q_2}(\mathbb{R}^d,w_2)$. Here $B^s_{p,q}(\mathbb{R}^d,w)$ denotes a weighted Besov space. We present a general approach which allows us to work with a large class of weights.

Keywords

Primary 41A4646E35smooth weightsindicesweighted Besov spacescompact embeddingsentropy numbers
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 2 , June 2006 , pp. 331 - 359
Copyright
Copyright © Edinburgh Mathematical Society 2006