Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

0460329 - MÚ 2017 RIV GB eng J - Journal Article
Caetano, A.M. - Gogatishvili, Amiran - Opic, B.
Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces.
Proceedings of the Royal Society of Edinburgh. A - Mathematics. Roč. 146, č. 5 (2016), s. 905-927. ISSN 0308-2105. E-ISSN 1473-7124
R&D Projects: GA ČR GA13-14743S
Institutional support: RVO:67985840
Keywords : quasi-Banach function space * compactness * compact embedding
Subject RIV: BA - General Mathematics
Impact factor: 1.158, year: 2016
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10379393&fileId=S0308210515000761

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn ), 1 ≤ p < ∞, 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, 0 < s < 1, 0 < p,q ≤ ∞, into Lorentz-type spaces.
Permanent Link: http://hdl.handle.net/11104/0260448