Traces of functions with a dominating mixed derivative in ℝ 3

Jan Vybíral; Winfried Sickel

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1239-1273
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Vybíral, Jan, and Sickel, Winfried. "Traces of functions with a dominating mixed derivative in $\mathbb {R}^3$." Czechoslovak Mathematical Journal 57.4 (2007): 1239-1273. <http://eudml.org/doc/31191>.

@article{Vybíral2007,
abstract = {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.},
author = {Vybíral, Jan, Sickel, Winfried},
journal = {Czechoslovak Mathematical Journal},
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},
language = {eng},
number = {4},
pages = {1239-1273},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Traces of functions with a dominating mixed derivative in $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/31191},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Vybíral, Jan
AU - Sickel, Winfried
TI - Traces of functions with a dominating mixed derivative in $\mathbb {R}^3$
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1239
EP - 1273
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/31191
ER -

References

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