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Zeitschrift für Analysis und ihre Anwendungen


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Volume 25, Issue 1, 2006, pp. 73–80
DOI: 10.4171/ZAA/1278

Published online: 2006-03-31

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

David E. Edmunds[1], Petr Gurka[2] and Bohumír Opic[3]

(1) University of Sussex, Brighton, United Kingdom
(2) Czech University of Life Sciences, Prague, Czech Republic
(3) Czech Academy of Sciences, Prague, Czech Republic

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 $\sigma$ less than one into a space of $\lambda(\cdot)$-H\"older-continuous functions. We show that such an embedding is not compact and that it is sharp.

Keywords: Lorentz-Zygmund spaces, logarithmic Bessel potential spaces, Hölder-continuous functions, embeddings

Edmunds David, Gurka Petr, Opic Bohumír: Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces. Z. Anal. Anwend. 25 (2006), 73-80. doi: 10.4171/ZAA/1278