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Compact embeddings of Brézis-Wainger type.

Fernando CobosThomas KühnTomas Schonbek — 2006

Revista Matemática Iberoamericana

Let Ω be a bounded domain in R and denote by id the restriction operator from the Besov space B (R) into the generalized Lipschitz space Lip(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like e(id) ~ k if α > max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.

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