Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis

TL;DR

This paper proves new nonlinear Brascamp-Lieb inequalities invariant under diffeomorphisms using induction-on-scales, with applications to multilinear convolution inequalities and Fourier restriction theory in higher dimensions.

Contribution

It introduces a novel method for establishing nonlinear Brascamp-Lieb inequalities and extends recent multilinear harmonic analysis results to higher dimensions.

Findings

Proved diffeomorphism invariant nonlinear Brascamp-Lieb inequalities.

Extended multilinear convolution inequalities to higher dimensions.

Enhanced Fourier restriction theory with new inequalities.

Abstract

We use the method of induction-on-scales to prove certain diffeomorphism invariant nonlinear Brascamp--Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru--Herr--Tataru and Bennett--Carbery--Wright.