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

  • António Caetano (a1), Amiran Gogatishvili (a2) and Bohumír Opic (a3)

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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 (ℝ n ), 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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