Equivalence of anchored and ANOVA spaces via interpolation

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