A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions

We show that the Fourier extension conjecture on the paraboloid in three dimensions is equivalent to a local single scale smooth Alpert trilinear inequality, which is an improvement of an analogous multiscale trilinear inequality in arXiv:2506.03992.

Publication Details

Journal
ArXiv.org
Published
2025-06-29
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions

ArXiv.org
Nonlinear Partial Differential Equations
article

A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions

article en

Abstract

We show that the Fourier extension conjecture on the paraboloid in three dimensions is equivalent to a local single scale smooth Alpert trilinear inequality, which is an improvement of an analogous multiscale trilinear inequality in arXiv:2506.03992.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 40%
Nonlinear Partial Differential Equations
Open Access PDFOpenAlex
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A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions · ArXiv.org (2025) | TGRS Research Map | TGRS