Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases. Issue 2 (2011)

• Record Type: Journal Article
• Authors: Haroske Haroske, Dorothee D. Dorothee D.; Skrzypczak Skrzypczak, Leszek Leszek
• Other Names: Triebel Triebel Hans Hans Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 9:Issue 2(2011)
• Page Start: 129
• Page End: 178
• Publication Date: 2011
• Subjects: Besov spaces, Triebel-Lizorkin spaces, Muckenhoupt weights, compact embeddings, entropy numbers; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2011/928962
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt A p 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.