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arXiv · 2509.07624

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

Maciej Rzeszut
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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.

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Maciej Rzeszut. 2025-09-09. Disjointification inequalities for Hoeffding subspaces of $H^1$ on an infinite polydisc. https://arxiv.org/abs/2509.07624

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