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

TL;DR

This paper establishes a precise square function estimate for the cone in three-dimensional space, leading to progress on the local smoothing conjecture for the wave equation in two spatial and one time dimension.

Contribution

It provides a sharp square function estimate for the cone in b2^3, advancing the understanding of local smoothing for the wave equation in 2+1 dimensions.

Findings

Proved a sharp square function estimate for the cone in b2^3

Confirmed the local smoothing conjecture for the wave equation in 2+1 dimensions

Enhanced the theoretical framework for harmonic analysis related to wave equations

Abstract

We prove a sharp square function estimate for the cone in $\mathbb{R}^3$ and consequently the local smoothing conjecture for the wave equation in $2+1$ dimensions.