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

by    W. Farkas, J. Johnsen, W. Sickel

Preprint series: 99-18, Analysis

The paper is published: Math. Bohem., 125 (1), 1-37, 2000

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

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 trace are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the previously untreated cases.
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.

Upload: 1999-03-05

Update: 2000-03-24

The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.