Abstract
AbstractWe prove a variable coefficient version of the square function estimate of GuthβWangβZhang. By a classical argument of MockenhauptβSeegerβSogge, it implies the full range of sharp local smoothing estimates for βdimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is settled.
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