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Article Dans Une Revue The Journal of Geometric Analysis Année : 2021

Littlewood-Paley-Stein Functions for Hodge-de Rham and Schrödinger Operators

Thomas Cometx

Résumé

We study the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schrödinger 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 Schrödinger operators on L p .
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Dates et versions

hal-02416797 , version 1 (17-12-2019)

Identifiants

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Thomas Cometx. Littlewood-Paley-Stein Functions for Hodge-de Rham and Schrödinger Operators. The Journal of Geometric Analysis, In press, ⟨10.1007/s12220-020-00569-x⟩. ⟨hal-02416797⟩
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