Uniform Convolution and Fourier Restriction estimates for complex polynomial curves in ℂ³

2020/12/17 by Conor Meade, Meade, Conor
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2012.09651

openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish optimal (p,q) ranges for two types of estimates associated to three dimensional complex polynomial curves. These are the estimates for the weighted restriction of the Fourier Transform to a complex polynomial curve, and the weighted Convolution Operator associated to a complex polynomial curve. Establishing these estimates comes down to establishing a lower bound for the Jacobian of a mapping associated to the complex curve in question.

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