Geodesic
L p Boundedness of the Riesz transform related to Schrödinger operators on a manifold
Badr, Nadine1 ; Ben Ali, Besma2 
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
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 725-765

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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 
@article{ASNSP_2009_5_8_4_725_0,
     author = {Badr, Nadine and Ben Ali, Besma},
     title = {$L^{p}$ {Boundedness} of the {Riesz} transform related to {Schr\"odinger} operators on a manifold},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {725--765},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {4},
     year = {2009},
     mrnumber = {2647910},
     zbl = {1200.35060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/}
}
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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, Série 5, Tome 8 (2009) no. 4, pp. 725-765. http://geodesic.mathdoc.fr/item/ASNSP_2009_5_8_4_725_0/