Compact Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving -Modulus of Smoothness

  • Amiran Gogatishvili

    Czech Academy of Sciences, Prague, Czech Republic
  • Júlio S. Neves

    Universidade de Coimbra, Portugal
  • Bohumír Opic

    Czech Academy of Sciences, Prague, Czech Republic

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