CONCERNING Lp RESOLVENT ESTIMATES FOR SIMPLY CONNECTED MANIFOLDS OF CONSTANT CURVATURE

Abstract. We prove families of uniform (Lr, Ls) resolvent estimates for simply con-nected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean space of Kenig, Ruiz and the second author [6]. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem. 1. Introduction an