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

Details $L^{p}$ Boundedness of Riesz transform related to Schrödinger operators on a manifold $L^{p}$ Boundedness of Riesz transform related to Schrödinger operators on a manifold

2008-12-06

arxiv.org/abs/0812.1265v1

Mathematics

Differential Geometry

38 pages

Scientific paper

We establish various $L^{p}$ estimates for the Schr\"odinger operator
$-\Delta+V$ on Riemannian manifolds satisfying the doubling property and a
Poincar\'e inequality, where $\Delta $ is the Laplace-Beltrami operator and $V$
belongs to a reverse H\"{o}lder class. At the end of this paper we apply our
result on Lie groups with polynomial growth.

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