Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 111-138

ENTROPY AND APPROXIMATION NUMBERS OF EMBEDDINGS OF FUNCTION SPACES WITH MUCKENHOUPT WEIGHTS, II. GENERAL WEIGHTS

Dorothee D. Haroske and Leszek Skrzypczak

Friedrich-Schiller-University Jena, Mathematical Institute
D-07737 Jena, Germany; dorothee.haroske 'at' uni-jena.de

Adam Mickiewicz University, Faculty of Mathematics and Computer Science
Ul. Umultowska 87, 61-614 Poznan, Poland; lskrzyp 'at' amu.edu.pl

Abstract. We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weights belong to Muckenhoupt A_p classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.

2000 Mathematics Subject Classification: Primary 46E35, 42B35, 41A46, 47B06.

Key words: Function spaces, Muckenhoupt weights, compact embeddings, entropy numbers, approximation numbers, singularities.

Reference to this article: D.D. Haroske and L. Skrzypczak: Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights. Ann. Acad. Sci. Fenn. Math. 36 (2011), 111-138.

Full document as PDF file

doi:10.5186/aasfm.2011.3607

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