Traces of functions with a dominating mixed derivative in 鈩?sup>3
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- 作者：Jan Vyb铆ral and Winfried Sickel
- 关键词：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
- 刊名：Czechoslovak Mathematical Journal
- 出版时间：December, 2007
- 出版年：2007
- 期刊代码：8_00114642
- 类别：ear
- 卷：57
- 期：4
- 页码：1239-1273
- 数据来源：sp
摘要
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.