Yakun Xi - Square function estimates and local smoothing for Fourier integral operators

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.

Видео Yakun Xi - Square function estimates and local smoothing for Fourier integral operators канала Fourier restriction online 2021