Disjointification inequalities for Hoeffding subspaces of $H^1$ on an infinite polydisc

Abstract

We prove that the $L^1$ norm on the linear span of functions on $\T^\N$ dependent on $m$ variables and analytic and mean zero in each of them can be expressed as an interpolation sum of $H^1\left({\mathbb{T}}^S,{\ell }^1\left({\mathbb{N}}^S,H^2\left({\mathbb{T}}^{[1,m]\setminus S},{\ell }^2\left({\mathbb{N}}^{[1,m]\setminus S}\right)\right)\right)\right)$ norms over $S\subseteq [1,m]$ and derive some interpolation consequences.