  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.
