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

Entropy and Approximation Numbers

of Embeddings of Function Spaces

with Muckenhoupt Weights, I

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 |

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 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.