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Zbl 1078.46022
Haroske, Dorothee D.; Triebel, Hans
Wavelet bases and entropy numbers in weighted function spaces. (English)
[J] Math. Nachr. 278, No. 1-2, 108-132 (2005). ISSN 0025-584X; ISSN 1522-2616/e

The authors develop the theory of inhomogeneous representations of function spaces of type $$B^s_{pq}(\bbfR^N, w)\text{ and }F^s_{pq}(\bbfR^N, w),\quad s\in\bbfR,\quad 0< p,\,q\le\infty,$$ where $w$ is a smooth weight of polynomial type without local singularities. If $p<\infty$, $q<\infty$, then these representations are unconditional Schauder bases. Moreover, the authors deal with entropy numbers in weighted sequence spaces. More precisely, using the results mentioned above they present estimates of entropy numbers of compact embeddings between these spaces.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *46E35 Sobolev spaces and generalizations
42C40 Wavelets
42B35 Function spaces arising in harmonic analysis
41A46 Approximation by arbitrary nonlinear expressions
47B06 Riesz operators and eigenvalue distributions

Keywords: wavelet bases; weighted function spaces; entropy numbers

Cited in: Zbl 1130.46020

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