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Square function estimates and Local smoothing for Fourier Integral Operators

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arxiv 2010.14390 v2 pith:3TBIXOPV submitted 2020-10-27 math.AP math.CA

Chuanwei Gao , Bochen Liu , Changxing Miao , Yakun Xi This is my paper · ORCID
classification math.APmath.CA
keywords localsmoothingestimatesfourierfunctionintegraloperatorssquare
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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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