The Endpoint Perturbed Brascamp-Lieb Inequality with Examples

TL;DR

This paper proves the endpoint multilinear Brascamp-Lieb inequality and its variants, extending the results to perturbed inequalities with examples, advancing understanding of multilinear integral inequalities.

Contribution

It establishes the endpoint multilinear Brascamp-Lieb inequality and generalizes it to perturbed versions, providing new theoretical insights and techniques.

Findings

Proved the endpoint multilinear Brascamp-Lieb inequality.

Extended results to endpoint multilinear $k_j$-variety theorem.

Generalized to endpoint perturbed Brascamp-Lieb inequalities.

Abstract

We prove the folklore endpoint multilinear $k_j$-plane conjecture originated from the paper \cite{bennett2006multilinear} of Bennett, Carbery and Tao. Along the way we prove a more general result, namely the endpoint multilinear $k_j$-variety theorem. Finally, we generalize our results to the endpoint perturbed Beascamp-Lieb inequality using techniques in this paper.