Full paper in PDF format:
$%D. D. Haroske and L. Skrzypczak, Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I, Rev. Mat. Complut. 21 (2008), no. 1, 135–177.%$

Entropy and Approximation Numbers
of Embeddings of Function Spaces
with Muckenhoupt Weights, I
Dorothee D. HAROSKE and Leszek SKRZYPCZAK
Mathematical Institute
Friedrich-Schiller-University Jena
D-07737 Jena — Germany
haroske@minet.uni-jena.de
Faculty of Mathematics & Computer Science
Adam Mickiewicz University
Ul. Umultowska 87
61-614 Poznań — Poland
lskrzyp@amu.edu.pl

Received: July 10, 2007
Accepted: August 30, 2007

ABSTRACT

We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt Ap class. For weights of purely polynomial growth, both near some singular point and at infinity, we obtain sharp asymptotic estimates for the entropy numbers and approximation numbers of this embedding. The main tool is a discretization in terms of wavelet bases.

Key words: wavelet bases, Muckenhoupt weighted function spaces, compact embeddings, entropy numbers, approximation numbers.
2000 Mathematics Subject Classification: 46E35, 42C40, 42B35, 41A46, 47B06.