JournalszaaVol. 25, No. 1pp. 73–80

Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces

  • David E. Edmunds

    University of Sussex, Brighton, United Kingdom
  • Petr Gurka

    Czech University of Life Sciences, Prague, Czech Republic
  • Bohumír Opic

    Czech Academy of Sciences, Prague, Czech Republic
Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces cover
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Abstract

In our recent paper [Compact and continuous embeddings of logarithmic Bessel potential spaces. Studia Math.~168 (2005), 229 -- 250] we have proved an embedding of a logarithmic Bessel potential space with order of smoothness σ\sigma less than one into a space of λ()\lambda(\cdot)-H\"older-continuous functions. We show that such an embedding is not compact and that it is sharp.

Cite this article

David E. Edmunds, Petr Gurka, Bohumír Opic, Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces. Z. Anal. Anwend. 25 (2006), no. 1, pp. 73–80

DOI 10.4171/ZAA/1278