${L}^{p}$ 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, p. 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.

Classification:  35J10,  42B37
@article{ASNSP_2009_5_8_4_725_0,
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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {4},
year = {2009},
pages = {725-765},
zbl = {1200.35060},
mrnumber = {2647910},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_4_725_0}
}

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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