A sharp square function estimate for the moment curve in ℝⁿ

2023/09/24 by Larry Guth, Guth, Larry, Dominique Maldague +1
Mathematics · Computer Science · #Mathematical Approximation and Integration #Advanced Mathematical Modeling in Engineering #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2309.13759

Abstract

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to C_εR^ε) square function estimates for the moment curve (t,t²,…,tⁿ) in ℝⁿ. Our inductive scheme incorporates sharp square function estimates for auxiliary conical sets, which allows us to fully exploit lower dimensional information.

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