Non-Transversal Multilinear Duality and Joints (2203.02320v2)

Published 4 Mar 2022 in math.FA, math.CA, math.CO, and math.MG

Abstract: We develop a framework for a duality theory for general multilinear operators which extends that for transversal multilinear operators which has been established in arXiv:1809.02449. 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 (arXiv:0811.2251 and arXiv:1012.3760) from the Euclidean setting.

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