Convolution Estimates for Singular Measures and Some Global Nonlinear Brascamp-Lieb Inequalities

Abstract

We give a $L^2\times L^2\to L^2$ convolution estimate for singular measures supported on transversal hypersurfaces in ${\mathbb{R}}^n$, which improves earlier results of Bejenaru, Herr & Tataru as well as Bejenaru & Herr. The arising quantities are relevant in the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp-Lieb inequalities with explicit constants in the same spirit.

11 pages