Multilinear singular operators with fractional rank

Abstract

We prove bounds for multilinear operators on ${\mathbb{R}}^d$ given by multipliers which are singular along a $k$ dimensional subspace. The new case of interest is when the rank $k/d$ is not an integer. Connections with the concept of {\em true complexity} from Additive Combinatorics are also investigated.

28 pages, 0 figures