MATHEMATICA BOHEMICA, Vol. 125, No. 1, pp. 1-37 (2000)

Traces of anisotropic Besov-Lizorkin-Triebel spaces—a complete treatment of the borderline cases

Walter Farkas, Jon Johnsen, Winfried Sickel

Walter Farkas, Inst. Theor. Informatics and Mathematics, Univ. Fed. Armed Forces Munich, Werner-Heisenberg-Weg 39, D–85577 Neubiberg, Germany
Jon Johnsen, Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7E, DK–9220 Aalborg O, Denmark, e-mail: jjohnsen@math.auc.dk
Winfried Sickel, Mathematics Department, Friedrich-Schiller-University Jena, Ernst-Abbe-Platz 1–4, D–07743 Jena, Germany, e-mail: sickel@minet.uni-jena.de

Abstract: Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev embeddings of J. Franke and B. Jawerth to the anisotropic scales.

Keywords: anisotropic Besov and Lizorkin-Triebel spaces, approximation spaces, trace operators, boundary problems, interpolation, atomic decompositions, refined Sobolev embeddings

Classification (MSC2000): 46E35

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