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Traces of functions with a dominating mixed derivative in ℝ3

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Abstract

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ3, 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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Authors and Affiliations

  1. Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany

    Jan Vybíral & Winfried Sickel

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  1. Jan Vybíral
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  2. Winfried Sickel
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Correspondence to Jan Vybíral.

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Vybíral, J., Sickel, W. Traces of functions with a dominating mixed derivative in ℝ3 . Czech Math J 57, 1239–1273 (2007). https://doi.org/10.1007/s10587-007-0122-0

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  • DOI: https://doi.org/10.1007/s10587-007-0122-0

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