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

Nadine Badr; Besma Ben Ali

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arXiv · 0812.1265

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

Nadine Badr·Besma Ben Ali

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Abstract

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 on Lie groups with polynomial growth.

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BibTeX RIS

Nadine Badr, Besma Ben Ali. 2008-12-06. $L^{p}$ Boundedness of Riesz transform related to Schrödinger operators on a manifold. https://arxiv.org/abs/0812.1265

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