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

### 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.

## Authors

Larry Guth

Massachusetts Institute of Technology, Cambridge, MA

Hong Wang

Institute for Advanced Study, Princeton, NJ

Ruixiang Zhang