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

Authors:
Dorothee D. Haroske;Susana D. Moura
Affiliations:
Mathematishes Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz I-4, D-07740 Jena, Germany;Departamento de Matemática, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal
Venue:
Journal of Approximation Theory
Year:
2004

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Abstract

We study continuity envelopes in spaces of generalised smoothness Bpq(s,Ψ) and Fpq(s,Ψ) and give some new characterisations for spaces Bpq(s,Ψ) The results are applied to obtain sharp asymptotic estimates for approximation numbers of compact embeddings of type id: Bpq(s1,Ψ) (U) → Bx-xs2 (U), Where n/p s1-s2 n/p+1 and U stands for the unit ball in Rn In case of entropy numbers we can prove two-sided estimates.