The endpoint perturbed Brascamp–Lieb inequalities with examples

Zhang, Ruixiang

doi:10.2140/apde.2018.11.555

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The endpoint perturbed Brascamp–Lieb inequalities with examples

Ruixiang Zhang

Vol. 11 (2018), No. 3, 555–581

DOI: 10.2140/apde.2018.11.555

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.

Keywords

Brascamp–Lieb inequality, polynomial method

Mathematical Subject Classification 2010

Primary: 42B10

Milestones

Received: 3 May 2016

Revised: 17 May 2017

Accepted: 29 September 2017

Published: 22 November 2017

Authors

Ruixiang Zhang
School of Mathematics Institute for Advanced Study Princeton, NJ United States

Vol. 11, No. 3, 2018