Stability of the Brascamp-Lieb constant and applications

Abstract

We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp-Lieb inequality which have arisen recently in harmonic analysis.

References in corpus (4)

• Convolutions of singular measures and applications to the Zakharov system
• A short proof of the multilinear Kakeya inequality
• Optimal mean value estimates for the quadratic Weyl sums in two dimensions
• Decoupling for perturbed cones and mean square of $|\zeta (\frac{1}{2}+it)|$

Cited by in corpus (14)

• On the nonlinear Brascamp-Lieb inequality
• On integer solutions of Parsell-Vinogradov systems
• Behaviour of the Brascamp--Lieb constant
• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• Sharp $L^p$ bounds for the helical maximal function
• Kakeya-Brascamp-Lieb inequalities
• Decoupling inequalities for quadratic forms
• Strengthened inequalities for the mean width and the $\ell$-norm
• Sharp decouplings for three dimensional manifolds in ${\mathbb{R}}^5$
• The nonlinear Brascamp-Lieb inequality for simple data
• Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies
• An Algebraic Brascamp-Lieb Inequality
• A new approach to the Fourier extension problem for the paraboloid
• Quiver Brascamp-Lieb inequalities