Estimates for Brascamp-Lieb forms in $L^p$ spaces with power weights

TL;DR

This paper derives near-optimal necessary and sufficient conditions for the boundedness of Brascamp-Lieb forms in weighted and Lorentz spaces, advancing the understanding of their behavior in these function spaces.

Contribution

It provides new near-optimal criteria for the boundedness of Brascamp-Lieb forms in weighted and Lorentz spaces, extending previous results.

Findings

Established necessary and sufficient conditions for boundedness.

Conditions are close to optimal.

Applicable to Lorentz and weighted $L^p$ spaces.

Abstract

We establish a set of necessary conditions and a set of sufficient conditions for boundedness of a family of Brascamp-Lieb forms in Lorentz spaces and $L^p$-spaces with power weights. The conditions are close to optimal.