Discrete nonlinear Hölder--Brascamp--Lieb inequalities: a local approach

Abstract

We study nonlinear Hölder--Brascamp--Lieb inequalities over ${\mathbb{Z}}^n$. Our method embeds the integers into a suitable compactification, over which local Hölder--Brascamp--Lieb theory may be applied (e.g heat flow). Our main result is a bound for multilinear Hölder--Brascamp--Lieb functionals over suitable sublattices in ${\mathbb{Z}}^n$.

70 pages