$L^p$ Boundedness of Riesz transform related to Schrödinger operators on a manifold

Abstract

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

arXiv comment38 pages

References in corpus (1)

• Real interpoaltion of Sobolev spaces associated to a weight

Cited by in corpus (1)

• Maximal Inequalities and Riesz Transform Estimates on $L^p$ Spaces for Magnetic Schrodinger Operators I