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

Walter Farkas;  Jon Johnsen;  Winfried Sickel — 2000

Mathematica Bohemica

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...

Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

Walter Farkas;  Niels Jacob;  René L. Schilling — 2001

We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) L p -variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the...

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