On local smoothing estimates for wave equations

Abstract

We prove sharp local smoothing estimates for wave equations on compact Riemannian manifolds in $n+1$ dimensions for odd $n$ and obtain improved estimates in even dimensions. This is achieved by deriving local smoothing estimates for certain Fourier integral operators. We also obtain improved local smoothing estimates for wave equations in Euclidean spaces.

Main results improved; Danqing He and Xiaochun Li are now named authors