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arXiv · 1610.07075

Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in $L_p$

Michael Gnewuch·Mario Hefter·Aicke Hinrichs·Klaus Ritter·Grzegorz W. Wasilkowski
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Abstract

We consider $\gamma$-weighted anchored and ANOVA spaces of functions with mixed first order partial derivatives bounded in a weighted $L_p$ norm with $1 \leq p \leq \infty$. The domain of the functions is $D^d$, where $D \subseteq \mathbb{R}$ 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 $D^d$.

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Michael Gnewuch, Mario Hefter, Aicke Hinrichs, Klaus Ritter, Grzegorz W. Wasilkowski. 2016-10-22. Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in $L_p$. https://arxiv.org/abs/1610.07075

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