Square function estimates and Local smoothing for Fourier Integral Operators
Analysis of PDEs
2023-04-11 v2 Classical Analysis and ODEs
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 completely settled.
Cite
@article{arxiv.2010.14390,
title = {Square function estimates and Local smoothing for Fourier Integral Operators},
author = {Chuanwei Gao and Bochen Liu and Changxing Miao and Yakun Xi},
journal= {arXiv preprint arXiv:2010.14390},
year = {2023}
}
Comments
39 pages, 3 figures, Referees' suggestions incorporated. To appear in Proc. Lond. Math. Soc