Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds

We prove high energy estimates for the boundary values of the weighted resolvent of the Laplacian on an asymptotically hyperbolic manifold. Our point is to use weights that fit the pseudo-differential calculus associated with the asymptotically hyperbolic geometry. Our proof is a combination of a trick using Mourre theory and of results by Froese-Hislop and Cardoso-Vodev.