L p Boundedness of the Riesz transform related to Schrödinger operators on a manifold
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 4, pp. 725-765.

We establish various L p estimates for the Schrödinger operator -Δ+V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where Δ 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.

Classification: 35J10, 42B37
Badr, Nadine 1; Ben Ali, Besma 2

1 Institut Camille Jordan, Université Claude Bernard Lyon 1, UMR du CNRS 5208, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne cedex, France
2 Université de Paris-Sud, UMR du CNRS 8628, F-91405 Orsay cedex, France
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Badr, Nadine; Ben Ali, Besma. $L^{p}$ Boundedness of the Riesz transform related to Schrödinger operators on a manifold. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 8 (2009) no. 4, pp. 725-765. http://www.numdam.org/item/ASNSP_2009_5_8_4_725_0/

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