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arXiv · 1912.08471

Littlewood-Paley-Stein functions for Hodge-de Rham and Schr{\"o}dinger operators

Thomas Cometx
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Abstract

We study the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schr{\"o}dinger operators on Riemannian manifolds. Under conditions on the Ricci curvature we prove their boundedness on L p for p in some interval (p 1 , 2] and make a link to the Riesz Transform. An important fact is that we do not make assumptions of doubling measure or estimates on the heat kernel in this case. For p > 2 we give a criterion to obtain the boundedness of the vertical Littlewood-Paley-Stein function associated with Schr{\"o}dinger operators on L p .

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Thomas Cometx. 2019-12-18. Littlewood-Paley-Stein functions for Hodge-de Rham and Schr{\"o}dinger operators. https://arxiv.org/abs/1912.08471

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