Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L-p

Gnewuch M.; Hefter M.; Hinrichs A.; Ritter K.; Wasilkowski G. W.

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Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L-p

机译：L-p中一阶混合光滑度的加权锚函数和ANOVA函数空间的等价性

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摘要

We consider gamma-weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in a weighted L-p, norm with 1 <= p <= infinity. The domain of the functions is D-d, where D subset of R is a bounded or unbounded interval. We provide conditions on the weights gamma that guarantee that anchored and ANOVA spaces are equal (as sets of functions) and have equivalent norms with equivalence constants uniformly or polynomially bounded in d. Moreover, we discuss applications of these results to integration and approximation of functions on D-d. (C) 2017 Elsevier Inc. All rights reserved.

机译：我们考虑具有混合一阶偏导数的函数的伽玛加权锚定空间和方差分析空间，它们的加权L-p范数为1 <= p <=无穷大。函数的域是D-d，其中R的D子集是有界或无界区间。我们提供权重伽玛的条件，以确保锚定空间和ANOVA空间相等（作为函数集），并且具有等价常数，且等价常数均匀或多项式地限定在d中。此外，我们讨论了这些结果在D-d上函数的积分和逼近中的应用。（C）2017 Elsevier Inc.保留所有权利。

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来源
《Journal of complexity》 |2017年第6期|78-99|共22页
作者
Gnewuch M.; Hefter M.; Hinrichs A.; Ritter K.; Wasilkowski G. W.;
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作者单位

Christian Albrechts Univ Kiel, Math Seminar, Ludewig Meyn Str 4, D-24098 Kiel, Germany;

Tech Univ Kaiserslautern, Fachbereich Math, Postfach 3049, D-67653 Kaiserslautern, Germany;

Johannes Kepler Univ Linz, Inst Anal, Altenberger Str 69, A-4040 Linz, Austria;

Tech Univ Kaiserslautern, Fachbereich Math, Postfach 3049, D-67653 Kaiserslautern, Germany;

Univ Kentucky, Dept Comp Sci, Davis Marksbury Bldg,329 Rose St, Lexington, KY 40506 USA;

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正文语种 eng
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关键词
Anchored decomposition; ANOVA decomposition; Tractability of multivariate problems; Sobolev spaces; Unbounded domains; General weights;

机译：锚定分解;ANOVA分解;多元问题的可牵引性;Sobolev空间;无界域;一般权重;

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专利

1. On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L-1 or L-infinity [J] . Hefter M., Ritter K., Wasilkowski G. W. Journal of complexity . 2016,第1期

机译：关于L-1或L-无穷大中混合光滑度为1的函数的加权锚定空间和ANOVA空间的等价性
2. A note on equivalence of anchored and ANOVA spaces; lower bounds [J] . Kritzer Peter, Pillichshammer Friedrich, Wasilkowski G. W. Journal of complexity . 2017,第feba期

机译：关于锚定空间和方差分析空间的等效性的注释；下界
3. Equivalence of anchored and ANOVA spaces via interpolation [J] . Hinrichs Aicke, Schneider Jan Journal of complexity . 2016,第Apra期

机译：通过插值等效的锚定空间和ANOVA空间
4. The Equivalence of Mann and Implicit Mann Iterations for Uniformly Pseudo-contractive Mappings in Uniformly Smooth Banach Spaces [C] . Cheng Wang, Zhiming Wang International Conference on Intelligent Structure and Vibration Control . 2011

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5. Weighted Composition Operators from Analytic Function Spaces into a Class of Weighted-type Banach Spaces [D] . Alyusof, Shams. 2020

机译：来自分析功能空间的加权组成算子进入一类加权型Banach空间
6. SMOOTHED ANOVA WITH SPATIAL EFFECTS AS A COMPETITOR TO MCAR IN MULTIVARIATE SPATIAL SMOOTHING [O] . Yufen Zhang, James S. Hodges, Sudipto Banerjee -1

机译：具有空间效应的平滑方差分析可作为多元空间平滑中MCAR的竞争者
7. Equivalence of anchored and ANOVA spaces via interpolation [O] . Hinrichs, Aicke, Schneider, Jan 2015

机译：通过插值的锚定和aNOVa空间的等价性

Equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in L-p

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