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arXiv · 2010.14390

Square function estimates and Local smoothing for Fourier Integral Operators

Chuanwei Gao·Bochen Liu·Changxing Miao·Yakun Xi
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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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Chuanwei Gao, Bochen Liu, Changxing Miao, Yakun Xi. 2020-10-27. Square function estimates and Local smoothing for Fourier Integral Operators. https://arxiv.org/abs/2010.14390

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