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Optimality of embeddings of Bessel-potential-type spaces into Lorentz–Karamata spaces

Published online by Cambridge University Press:  12 July 2007

Amiran Gogatishvili ,
Bohumír Opic  and
Júlio S. Neves
Amiran Gogatishvili
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Z̆itná 25, 11567 Prague 1, Czech Republicgogatish@math.cas.cz;
Bohumír Opic
Affiliation:
Mathematical Institute, Academy of Sciences of the Czech Republic, Z̆itná 25, 11567 Prague 1, Czech Republicopic@math.cas.cz
Júlio S. Neves
Affiliation:
Departamento de Matemática da FCT, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal (jsn@mat.uc.pt)
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Abstract

We establish sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz–Karamata (LK) spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are LK spaces. As a consequence of our results, we get growth envelopes of Bessel-potential spaces modelled upon LK spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 6 , December 2004 , pp. 1127 - 1147
Copyright
Copyright © Royal Society of Edinburgh 2004

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