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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2011/928962 |
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| author | Dorothee D. Haroske Leszek Skrzypczak |
| author_facet | Dorothee D. Haroske Leszek Skrzypczak |
| author_sort | Dorothee D. Haroske |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-4540ddbcdbc241df99c2cc619560b98a |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-4540ddbcdbc241df99c2cc619560b98a2025-02-03T01:09:43ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2011/928962 |
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