Lp boundedness of Riesz transform related to Schroedinger operators on a manifold

Abstract

We establish various $L^{p}$ estimates for the Schrodinger operator $-\Delta+V$ on Riemannian manifolds satisfying the doubling property and a Poincare inequality, where $\Delta $ is the Laplace-Beltrami operator and $V$ belongs to a reverse H\{o}lder class. At the end of this paper we apply our result to Lie groups with polynomial growth.