Square function estimates and Local smoothing for Fourier Integral Operators

2020/10/27 by Gao, Chuanwei, Liu, Bochen, Miao, Changxing +1
#35L05 #35S30 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.14390

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 2+1 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.

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