Riesz transform on manifolds and Poincaré inequalities

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Abstract

We study the validity of the Lp inequality for the Riesz transform when p > 2 and of its reverse inequality when 1 < p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.

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Auscher, P., & Coulhon, T. (2005). Riesz transform on manifolds and Poincaré inequalities. Annali Della Scuola Normale - Classe Di Scienze, 4(3), 531–555. https://doi.org/10.2422/2036-2145.2005.3.07

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