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Sharpness of embeddings in logarithmic Bessel-potential spaces

Published online by Cambridge University Press:  14 November 2011

David E. Edmunds ,
Petr Gurka  and
Bohumír Opic
David E. Edmunds
Affiliation:
Centre for Mathematical Analysis and its Applications, University of Sussex, Falmer, Brighton BN1 9QH, England e-mail: [email protected]
Petr Gurka
Affiliation:
Department of Mathematics, Agricultural University, 160 21 Prague 6, Czech Republic e-mail: [email protected] (or [email protected])
Bohumír Opic
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1, Czech Republic e-mail: [email protected]
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Abstract

This paper is a continuation of [4], where embeddings of certain logarithmic Bessel-potential spaces (modelled upon generalised Lorentz-Zygmund spaces) in appropriate Orlicz spaces (with Young functions of single and double exponential type) were derived. The aim of this paper is to show that these embedding results are sharp in the sense of [8].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 995 - 1009
Copyright
Copyright © Royal Society of Edinburgh 1996

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