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Journal of Function Spaces and Applications
Volume 3 (2005), Issue 1, Pages 33-71

Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

1Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal
2Mathematical Institute, Friedrih-Shiller-University Jena, D-07737 Jena, Germany

Received 1 March 2004

Academic Editor: Hans Triebel

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Continuity envelopes for the spaces of generalised smoothness Bpq(s,Ψ)(n) and Fpq(s,Ψ)(n) are studied in the so-called supercritical s=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.