Continuity envelopes of spaces of generalised smoothness, entropy and approximation numbers

Abstract

We study continuity envelopes in spaces of generalised smoothness Bpq(s,[Psi]) and Fpq(s,[Psi]) and give some new characterisations for spaces Bpq(s,[Psi]). The results are applied to obtain sharp asymptotic estimates for approximation numbers of compact embeddings of type id:Bpq(s1,[Psi])(U)-->B[infinity][infinity]s2(U), where and U stands for the unit ball in . In case of entropy numbers we can prove two-sided estimates.