The endpoint perturbed Brascamp–Lieb inequalities with examples

Abstract

We prove the folklore endpoint multilinear $k_j$-plane conjecture originating in a paper of Bennett, Carbery and Tao where the almost sharp multilinear Kakeya estimate was proved. 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 Brascamp–Lieb inequalities using techniques in earlier sections.