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

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.

15 pages, updated version with minor changes suggested by referee. New material discussing multi-linear fractional integrals