Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces
Published online by Cambridge University Press: 23 June 2016
Extract
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 , into Lorentz-type spaces.
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MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 5 , October 2016 , pp. 905 - 927
- Copyright
- Copyright © Royal Society of Edinburgh 2016
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