Hessian of Bellman functions and uniqueness of Brascamp--Lieb inequality

Abstract

Under some assumptions on the vectors $a_1,..,a_n\in {\mathbb{R}}^k$ and the function $B:{\mathbb{R}}^n\to \mathbb{R}$ we find the sharp estimate of the expression ${\int }_{{\mathbb{R}}^k}B(u_1(a_1\cdot x),...,u_n(a_n\cdot x))dx$ in terms of ${\int }_{\mathbb{R}}{u}_j(y)dy,j=1,...,n.$ In some particular case we will show that these assumptions on $B$ imply that there is only one Brascamp--Lieb inequality.

16 pages

References in corpus (3)

• Point-to-point distance in first passage percolation on (tree) x Z
• Bellman partial differential equation and the hill property for classical isoperimetric problems
• Inequality for Burkholder's martingale transform

Cited by in corpus (3)

• Bellman partial differential equation and the hill property for classical isoperimetric problems
• Improving Beckner's bound via Hermite functions
• A Variation on Hölder-Brascamp-Lieb Inequalities