Equivalence of anchored and ANOVA spaces via interpolation

Abstract

We consider weighted anchored and ANOVA spaces of functions with first order mixed derivatives bounded in $L_p$. Recently, Hefter, Ritter and Wasilkowski established conditions on the weights in the cases $p=1$ and $p=\infty$ 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 $p\in [1,\infty ]$. It is shown how this can be achieved via interpolation.

12 pages, Version 2: several minor changes incorporating referee's suggestions

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