Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions
Cristian Rios, Eric Sawyer
Published: 2025/6/4
Abstract
We prove that a local trilinear extension inequality on the paraboloid in three dimensions is equivalent to the Fourier restriction conjecture, and then we prove a variant involving smooth Alpert wavelets that represents the weakest such inequality the authors could find that characterizes the Fourier extension conjecture.