OPTIMALITY OF EMBEDDINGS OF BESSEL-POTENTIAL-TYPE SPACES INTO GENERALIZED HÖLDER SPACES

OPTIMALITY OF EMBEDDINGS OF BESSEL-POTENTIAL-TYPE SPACES INTO GENERALIZED HÖLDER SPACES

We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Hölder spaces. As consequences of our results, we get continuous envelopes of Bessel...

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Bibliographic Details
Published in:Publicacions matemàtiques Vol. 49; no. 2; pp. 297 - 327
Main Authors: Gogatishvili, Amiran, Neves, Júlio S., Opic, Bohumír
Format: Journal Article
Language:English
Published: Universitat Autònoma de Barcelona 01-01-2005
Subjects:
Abstract spaces
Applied mathematics
Bedding
Continuous functions
Embeddings
Increasing functions
Mathematical functions
Mathematical theorems
Sobolev spaces
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Summary:We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Hölder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_49205_03