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.

arXiv commentv2: 39 pages, revised following the referee report

References in corpus (13)

• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Nested efficient congruencing and relatives of Vinogradov's mean value theorem
• Stability of the Brascamp-Lieb constant and applications
• A short proof of the multilinear Kakeya inequality
• Behaviour of the Brascamp--Lieb constant
• On integer solutions of Parsell-Vinogradov systems
• Discrete Fourier restriction via efficient congruencing: basic principles
• The Endpoint Perturbed Brascamp-Lieb Inequality with Examples
• Kakeya-Brascamp-Lieb inequalities
• The Cubic Case of Vinogradov's Mean Value Theorem --- A Simplified Approach to Wooley's "Efficient Congruencing"
• Additive equations in dense variables via truncated restriction estimates
• Solution-free sets for sums of binary forms
• A bilinear proof of decoupling for the cubic moment curve

Cited by in corpus (8)

• A short proof of ${\ell }^2$ decoupling for the moment curve
• Kakeya-Brascamp-Lieb inequalities
• Decoupling for certain quadratic surfaces of low co-dimensions
• Decoupling for two quadratic forms in three variables: a complete characterization
• A bilinear proof of decoupling for the cubic moment curve
• Decoupling inequalities for quadratic forms
• Regularized Brascamp--Lieb inequalities
• Burgess bounds for short character sums evaluated at forms II: the mixed case