A sharp square function estimate for the moment curve in $\mathbb{R}^3$

TL;DR

This paper establishes a precise $L^7$ square function estimate for the moment curve in three-dimensional space, advancing understanding of harmonic analysis related to this fundamental geometric object.

Contribution

It provides a sharp (up to epsilon losses) square function estimate for the moment curve in $R^3$, which was previously unknown.

Findings

Proves a sharp $L^7$ square function estimate for the moment curve.

Achieves near-optimal bounds up to $C_\e R^\e$ factors.

Enhances harmonic analysis techniques for geometric curves.

Abstract

We prove a sharp (up to $C_\epsilon R^\epsilon$) $L^7$ square function estimate for the moment curve in $\mathbb{R}^3$.