Bohumír Opic

Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness

Abstract We characterize local embeddings of Besov spaces B p , r 0 , b involving only a slowly varying smoothness b into classical Lorentz spaces. These results are applied to establish sharp local embeddings of the Besov spaces in question into Lorentz–Karamata spaces. As a consequence of these results, we are able to determine growth envelopes of spaces B p , r 0 , b and to show that we cannot describe all local embeddings of Besov spaces B p , r 0 , b into Lorentz–Karamata spaces in terms of growth envelopes.

Continuous and Compact Embeddings of Bessel-Potential-Type Spaces

We survey, comment and complement our results on embeddings of Bessel potential spaces modelled upon Lorentz–Karamata spaces. Target spaces in our embeddings are either Lorentz–Karamata spaces or generalized Holder spaces. In particular, we establish necessary and sufficient conditions both for continuous and compact embeddings of spaces in question.

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

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

Limiting variants of Krasnoselʼskiĭʼs compact interpolation theorem

L_p(\mathbb R^n)

Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces

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Interpolation of uniformly absolutely continuous operators

1 \leq p < \infty

Compact embeddings of besov spaces involving only slowly varying smoothness

, 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

Embeddings of Sobolev-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness

B^s_{p,q}(\mathbb R^n)

Sharp Hardy inequalities of fractional order involving slowly varying functions

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Compactness in quasi-Banach function spaces ∗

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