Geodesic
Traces of functions with a dominating mixed derivative in $\Bbb R^3$
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1239-1273 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 42B35, 46E35
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 
@article{CMJ_2007_57_4_a9,
     author = {Vyb{\'\i}ral, Jan and Sickel, Winfried},
     title = {Traces of functions with a dominating mixed derivative in $\Bbb R^3$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1239--1273},
     year = {2007},
     volume = {57},
     number = {4},
     mrnumber = {2357589},
     zbl = {1174.42027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a9/}
}
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Vybíral, Jan; Sickel, Winfried. Traces of functions with a dominating mixed derivative in $\Bbb R^3$. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1239-1273. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a9/