Discrete nonlinear H\"older--Brascamp--Lieb inequalities: a local approach

Ben Johnsrude

Discrete nonlinear H\"older--Brascamp--Lieb inequalities: a local approach

Classical Analysis and ODEs 2026-07-23 v1

Authors: Ben Johnsrude

Abstract

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

Keywords

Brascamp-Lieb inequalities discrete inequalities Hölder inequalities compactification multilinear functionals

Cite

@article{arxiv.2607.21864,
  title  = {Discrete nonlinear H\"older--Brascamp--Lieb inequalities: a local approach},
  author = {Ben Johnsrude},
  journal= {arXiv preprint arXiv:2607.21864},
  year   = {2026}
}

Comments

70 pages