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arXiv · 2506.03992

Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions

Cristian Rios·Eric Sawyer
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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.

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Cristian Rios, Eric Sawyer. 2025-06-04. Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions. https://arxiv.org/abs/2506.03992

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