Square function estimates and local smoothing for Fourier integral operators

Abstract

Abstract We prove a variable coefficient version of the square function estimate of Guth–Wang–Zhang. By a classical argument of Mockenhaupt–Seeger–Sogge, it implies the full range of sharp local smoothing estimates for ‐dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is settled.