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arXiv · 2309.13759

A sharp square function estimate for the moment curve in $\mathbb{R}^n$

Larry Guth·Dominique Maldague
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Abstract

We use high-low frequency methods developed in the context of decoupling to prove sharp (up to $C_\epsilon R^\epsilon$) square function estimates for the moment curve $(t,t^2,\ldots,t^n)$ in $\mathbb{R}^n$. 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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Larry Guth, Dominique Maldague. 2023-09-24. A sharp square function estimate for the moment curve in $\mathbb{R}^n$. https://arxiv.org/abs/2309.13759

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