Compact embeddings of Brézis-Wainger type

Let O be a bounded domain in Rn and denote by idO the restriction operator from the Besov space Bpq1+n/p(Rn) into the generalized Lipschitz space Lip(1,-a)(O). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idO) ~ k-1/p if a > max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.