| Abstract: |
| We prove sharp $L^p(dx) \to L^p(dtdx)$ local smoothing estimates for Fourier integral operators using the decoupling estimates of Bourgain and Demeter for the range $p\ge 2(n+1)/(n-1)$. These include bounds for solutions of wave equations on manifolds. We also show that for general FIOs satisfying the cinematic curvature assumption in our theorem, our results cannot be improved. |
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