Fourier decoupling for convex sequences

Abstract

We study the decoupling theory for functions on R with Fourier transform sup- ported in a neighborhood of a convex sequence [formula], where [formula] and 𝑔 : [0, 1] → R is a 𝐶² function satisfying 𝑔′(𝑥) > 0, 𝑔′′(𝑥) > 0 for every 𝑥 ∈ [0, 1]. We utilize the wave packet structure of functions with frequency support in a neigh- borhood of an arithmetic progression.