A note on equivalence of anchored and ANOVA spaces; lower bounds

We provide lower bounds for the norms of embeddings between γ-weighted anchored and ANOVA spaces of s-variate functions on [0,1]s with mixed partial derivatives of order one bounded in Lp norm (p∈[1,∞]). In particular we show that the norms behave polynomially in s for specific instances of finite order weights and finite diameter weights, and increase faster than any polynomial in s for product order-dependent weights.