Non-transversal multilinear duality and joints

Abstract

We develop a framework for a duality theory for general multilinear operators which extends that for transversal multilinear operators which has been established by Carbery, Hänninen and Valdimarsson (2022). 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 from the Euclidean setting.