Equivalence of anchored and ANOVA spaces via interpolation

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• 作者：Aicke Hinrichs^a ; ^{aicke.hinrichs@jku.at" class="auth_mail" title="E-mail the corresponding author} ; Jan Schneider^b ; ^{jan.schneider@uni-jena.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：ANOVA decomposition ; Anchored decomposition ; Norm equivalences
• 刊名：Journal of Complexity
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：33
• 期：Complete
• 页码：190-198
• 全文大小：391 K

文摘

We consider weighted anchored and ANOVA spaces of functions with first order mixed derivatives bounded in L_p$L_p$. Recently, Hefter, Ritter and Wasilkowski established conditions on the weights in the cases p=1$p=1$ and p=∞$p=\infty$ which ensure equivalence of the corresponding norms uniformly in the dimension or only polynomially dependent on the dimension. We extend these results to the whole range of p∈[1,∞]$p\in [1,\infty ]$. It is shown how this can be achieved via interpolation.