We establish various estimates for the Schrödinger operator on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where is the Laplace-Beltrami operator and belongs to a reverse Hölder class. At the end of this paper we apply our result to Lie groups with polynomial growth.
@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},
year = {2009},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {4},
mrnumber = {2647910},
zbl = {1200.35060},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2009_5_8_4_725_0/}
}
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AU - Badr, Nadine
AU - Ben Ali, Besma
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PY - 2009
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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. https://www.numdam.org/item/ASNSP_2009_5_8_4_725_0/
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