An Algebraic Brascamp-Lieb Inequality

Abstract

We prove a global nonlinear Brascamp-Lieb inequality for a general class of maps, encompassing polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that compensates for local degeneracies, and yields a uniform constant that depends only on the 'degree' of the maps involved.

References in corpus (14)

• Stability of the Brascamp-Lieb constant and applications
• On the nonlinear Brascamp-Lieb inequality
• On integer solutions of Parsell-Vinogradov systems
• Behaviour of the Brascamp--Lieb constant
• The Endpoint Perturbed Brascamp-Lieb Inequality with Examples
• The Hausdorff-Young inequality on Lie groups
• Kakeya-Brascamp-Lieb inequalities
• On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian groups
• On the Oberlin affine curvature condition
• Aspects of Multilinear Harmonic Analysis Related to Transversality
• A uniform Fourier restriction theorem for surfaces in R^d
• On $L^p$-improving for averages associated to mixed homogeneous polynomial hypersurfaces in ${\mathbb{R}}^3$
• $L^p$-improving estimates for Radon-like operators and the Kakeya-Brascamp-Lieb inequality
• An affine Fourier restriction theorem for conical surfaces