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

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 o...

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Main Authors:	Dorothee D. Haroske, Leszek Skrzypczak
Format:	Article
Language:	English
Published:	Hindawi Limited 2011-01-01
Series:	Journal of Function Spaces and Applications
Online Access:	http://dx.doi.org/10.1155/2011/928962

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spelling	doaj-4540ddbcdbc241df99c2cc619560b98a2020-11-24T23:15:50ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022011-01-019212917810.1155/2011/928962Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting casesDorothee D. Haroske0Leszek Skrzypczak1Mathematical Institute, Friedrich-Schiller-University Jena, D-07737 Jena, GermanyFaculty of Mathematics & Computer Science, Adam Mickiewicz University, Ul. Umultowska 87, 61-614 Poznań, PolandWe 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.http://dx.doi.org/10.1155/2011/928962
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dorothee D. Haroske Leszek Skrzypczak
spellingShingle	Dorothee D. Haroske Leszek Skrzypczak Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases Journal of Function Spaces and Applications
author_facet	Dorothee D. Haroske Leszek Skrzypczak
author_sort	Dorothee D. Haroske
title	Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases
title_short	Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases
title_full	Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases
title_fullStr	Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases
title_full_unstemmed	Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases
title_sort	entropy numbers of embeddings of function spaces with muckenhoupt weights, iii. some limiting cases
publisher	Hindawi Limited
series	Journal of Function Spaces and Applications
issn	0972-6802
publishDate	2011-01-01
description	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.
url	http://dx.doi.org/10.1155/2011/928962
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Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases

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