ON Lp RESOLVENT ESTIMATES FOR LAPLACE-BELTRAMI OPERATORS ON COMPACT MANIFOLDS

Abstract. In this article we prove Lp estimates for resolvents of La-place-Beltrami operators on compact Riemannian manifolds, generaliz-ing results of [12] in the Euclidean case and [17] for the torus. We follow [18] and construct Hadamard’s parametrix, then use classical bounded-ness results on integral operators with oscillatory kernels related to the Carleson and Sjölin condition. Our initial motivation was to obtain Lp Carleman estimates with limiting Carleman weights generalizing those of Jerison and Kenig [11]; we illustrate the pertinence of Lp resolvent esti-mates by showing the relation with Carleman estimates. Such estimates are useful in the construction of complex geometrical optics solutions to the Schrödinger equation with unbounded potentials, an essential devic