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We prove uniform   $L^p$   resolvent estimates for the stationary damped wave operator. The uniform   $L^p$   resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos Ferreira–Kenig–Salo [ 7 ] and advanced further by Bourgain–Shao–Sogge–Yao [ 2 ]. Here, we provide an alternative proof relying on the techniques of semiclassical Strichartz estimates. This approach allows us also to handle non-self-adjoint perturbations of the Laplacian and embeds very naturally in the semiclassical spectral analysis framework.

From Semiclassical Strichartz Estimates to Uniform $L^p$ Resolvent Estimates on Compact Manifolds