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

Larry Guth; Hong Wang; Ruixiang Zhang

doi:https://doi.org/10.4007/annals.2020.192.2.6

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

Pages 551-581 from Volume 192 (2020), Issue 2 by Larry Guth, Hong Wang, Ruixiang Zhang

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.

Mathematical Subject Classification

Primary 2000: 35L05, 42, 42B15 Secondary: 42B20, 42B25

Milestones

Received: 9 October 2019
Revised: 22 June 2020
Accepted: 22 June 2020
Published online: 9 September 2020

Authors

Larry Guth

Massachusetts Institute of Technology, Cambridge, MA

Hong Wang

Institute for Advanced Study, Princeton, NJ

Ruixiang Zhang

University of Wisconsin-Madison, Madison, WI