Square Function Estimates and Local Smoothing for Fourier Integral Operators
Time: 2020-12-07
Published By: He Liu
Speaker(s): Yakun Xi (Zhejiang University)
Time: 10:00-11:00 December 9, 2020
Venue: Room 9, Quan Zhai, BICMR
We discuss some recent progress on the local smoothing conjecture for FIOs. In particular, we prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang, which implies the full range of sharp local smoothing estimates for 2+1 dimensional Fourier integral operators satisfying the cinematic curvature condition. As a consequence, the local smoothing conjecture for wave equations on compact Riemannian surfaces is settled. This is a joint work with Chuanwei Gao, Bochen Liu and Changxing Miao.
