The Endpoint Perturbed Brascamp-Lieb Inequality with Examples

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.

Consequent progress on the endpoint multilinear restriction conjecture added as comments. Minor typos corrected

References in corpus (1)

• A short proof of the multilinear Kakeya inequality

Cited by in corpus (7)

• On the nonlinear Brascamp-Lieb inequality
• Behaviour of the Brascamp--Lieb constant
• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• Kakeya-Brascamp-Lieb inequalities
• Decoupling inequalities for quadratic forms
• Joints of varieties
• An Algebraic Brascamp-Lieb Inequality