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Journal of Function Spaces and Applications
Volume 9 (2011), Issue 2, Pages 129-178
http://dx.doi.org/10.1155/2011/928962

Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases

1Mathematical Institute, Friedrich-Schiller-University Jena, D-07737 Jena, Germany
2Faculty of Mathematics & Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, Poland

Received 1 July 2009

Academic Editor: Hans Triebel

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt Ap class. This extends our previous results [25] to more general weights of logarithmically disturbed polynomial growth, both near some singular point and at infinity. We obtain sharp asymptotic estimates for the entropy numbers of this embedding. Essential tools are a discretisation in terms of wavelet bases, as well as a refined study of associated embeddings in sequence spaces and interpolation arguments in endpoint situations.