Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/15979
 Title: Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces Author: Caetano, AntónioOpic, BohumírGogatishvili, Amiran Keywords: Quasi-Banach function spaceCompactnessCompact embeddingAbsolute continuityBesov spaceLorentz 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

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