Open Access
May, 2006 Compact embeddings of Brézis-Wainger type
Fernando Cobos , Thomas Kühn , Tomas Schonbek
Rev. Mat. Iberoamericana 22(1): 305-322 (May, 2006).


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.


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Fernando Cobos . Thomas Kühn . Tomas Schonbek . "Compact embeddings of Brézis-Wainger type." Rev. Mat. Iberoamericana 22 (1) 305 - 322, May, 2006.


Published: May, 2006
First available in Project Euclid: 24 May 2006

zbMATH: 1109.47015
MathSciNet: MR2268121

Primary: 46B50 , 46E35 , 47B06

Keywords: Besov spaces , compact embeddings , entropy numbers , Lipschitz spaces

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.22 • No. 1 • May, 2006
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