A short proof of ${\ell }^2$ decoupling for the moment curve

Abstract

We give a short and elementary proof of the ${\ell }^2$ decoupling inequality for the moment curve in ${\mathbb{R}}^k$, using a bilinear approach inspired by the nested efficient congruencing argument of Wooley (arXiv:1708.01220).

v3: fixed up issues about weights in the published version. Weights in Section 3 are now required to decay a bit faster at infinity, and proofs of properties of weights are now given in an Appendix

References in corpus (1)

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

Cited by in corpus (2)

• Decoupling for Schatten class operators in the setting of Quantum Harmonic Analysis
• Function spaces for decoupling