Compact embeddings of Brézis-Wainger type
Copyright policy )Compact embeddings of Brézis-Wainger type
Let \Omega be a bounded domain in \mathbb R^n and denote by id_\Omega the restriction operator from the Besov space B_{pq}^{1+n/p}(\mathbb R^n) into the generalized Lipschitz space Lip^{(1,-\alpha)}(\Omega) . We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like e_k(id_\Omega) \sim k^{-1/p} if \alpha > \max (1+2/p-1/q,1/p) . Our estimates improve previous results by Edmunds and Haroske.
- Leipzig University Germany
- Complutense University of Madrid Spain
- Florida Atlantic University United States
entropy numbers, Lipschitz spaces, Operators, 1202 Análisis y Análisis Funcional, Banach-Spaces, Entropy Numbers, Compactness in Banach (or normed) spaces, compact embeddings, 517.98, Compact embeddings, Besov spaces, 46B50, Análisis matemático, limiting embeddings, 47B06, 46E35, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematics, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
entropy numbers, Lipschitz spaces, Operators, 1202 Análisis y Análisis Funcional, Banach-Spaces, Entropy Numbers, Compactness in Banach (or normed) spaces, compact embeddings, 517.98, Compact embeddings, Besov spaces, 46B50, Análisis matemático, limiting embeddings, 47B06, 46E35, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Mathematics, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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