Estimates for a family of multi-linear forms

TL;DR

This paper characterizes the L^p spaces where certain multi-linear forms are bounded and applies this to analyze a non-linear map in scattering theory.

Contribution

It provides a new characterization of boundedness for a specific class of multi-linear forms and explores their application in scattering theory.

Findings

Identified the L^p spaces for boundedness of the forms

Applied the characterization to a non-linear map in scattering theory

Enhanced understanding of multi-linear forms in mathematical analysis

Abstract

We consider a special class of the multi-linear forms studied by Brascamp and Lieb. For these forms, we are able to characterize the L^p spaces for which the form is bounded. We use this characterization to study a non-linear map that arises in scattering theory.