Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems

Abstract

We prove $\ell^{p}L^{p}$ decoupling inequalities for a class of moment manifolds. These inequalities imply optimal mean value estimates for multidimensional Weyl sums of the kind considered by Arkhipov, Chubarikov, and Karatsuba and by Parsell. In our proofs we take a new point of view on the Bourgain--Demeter--Guth induction on scales argument. This point of view substantially simplifies even the proof of $\ell^{2}L^{p}$ decoupling for the moment curve.