Winfried Sickel, Jan Vybiral, Mathematisches Institut, Fakultat fur Mathematik und Informatik, Friedrich-Schiller-Universitat Jena, 07743 Jena, Germany, e-mail: vybiral@minet.uni-jena.de, sickel@minet.uni-jena.de
Abstract: We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in $\R^3$, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to $p=2$. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.
Keywords: Sobolev spaces of dominating mixed smoothness, Besov and Lizorkin-Triebel classes of dominating mixed smoothness, Fourier analytic characterizations, atomic decompositions, traces on hyperplanes in oblique position
Classification (MSC 2000): 42B35, 46E35
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