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

Badr, Nadine; Ben Ali, Besma

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 725-765.

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 to Lie groups with polynomial growth.

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