A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions

2024/11/27 by Sawyer, Eric T.
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.18457

Abstract

We compare the smooth Alpert testing condition for the paraboloid Fourier extension conjecture in RiSa3 to the modulated testing condition for the Kakeya conjecture in RiSa2. To this end, the modulated testing condition is converted to a certain restricted smooth Alpert testing condition for the paraboloid Fourier extension conjecture.

Related

• A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions
• Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions
• A refined trilinear Kakeya estimate in ℝ³
• On the restriction theorem for paraboloid in \mathbb R⁴
• Equivalence of linear and trilinear Kakeya conjectures in three dimensions