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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
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
Summary:
We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ${\mathbb{R}}^3$, 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.
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