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Title: Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces
Author: Caetano, António
Opic, Bohumír
Gogatishvili, Amiran
Keywords: Quasi-Banach function space
Compact embedding
Absolute continuity
Besov space
Lorentz space
Issue Date: 23-Jun-2016
Publisher: Cambridge University Press; Royal Society of Edinburgh
Abstract: There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0<s<1$, $0<p,q\leq \infty$, into Lorentz-type spaces.
Peer review: yes
DOI: 10.1017/S0308210515000761
ISSN: 0308-2105
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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