Compact Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving -Modulus of Smoothness
Amiran Gogatishvili
Czech Academy of Sciences, Prague, Czech RepublicJúlio S. Neves
Universidade de Coimbra, PortugalBohumír Opic
Czech Academy of Sciences, Prague, Czech Republic
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Abstract
We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces , modelled upon a rearrangement-invariant Banach function spaces , into generalized Hölder spaces involving k-modulus of smoothness. To this end, we derive a characterization of compact subsets of generalized Hölder spaces. We apply our results to the case when is a Lorentz–Karamata space . Applications cover both superlimiting and limiting cases.
Cite this article
Amiran Gogatishvili, Júlio S. Neves, Bohumír Opic, Compact Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving -Modulus of Smoothness. Z. Anal. Anwend. 30 (2011), no. 1, pp. 1–27
DOI 10.4171/ZAA/1421