Approximation and entropy numbers in Besov spaces of generalized smoothness

We determine the exact asymptotic behaviour of entropy and approximation numbers of the limiting restriction operator J : B-p,q1(s,psi)'(R-d) -> B-p,q2(s)(Omega), defined by J(f) = f vertical bar(n). Here Omega is a non-empty bounded domain in R-d, psi is an increasing slowly varying function, 0 < p < infinity, 0 < q(1),q(2) <= infinity, s is an element of R,and B-p,q1(s,psi)'(R-d) is the Besov space of generalized smoothness given by the function t(s)psi(t). Our results improve and extend those established by Leopold [Embeddings and entropy numbers in Besov spaces of generalized smoothness, in: Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, Marcel Dekker, New York, 2000, pp. 323-336]. (C) 2008 Elsevier Inc. All rights reserved.