Non-transversal multilinear duality and joints

Abstract

. We develop a framework for a duality theory for general multilin- ear operators which extends that for transversal multilinear operators which has been established in [4]. We apply it to the setting of joints and multijoints, and obtain a “factorisation” theorem which provides an analogue in the discrete setting of results of Bourgain and Guth ([7] and [2]) from the Euclidean setting.