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Square function estimates and Local smoothing for Fourier Integral Operators (2010.14390v2)
Published 27 Oct 2020 in math.AP and math.CA
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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