Riesz transform on manifolds and Poincaré inequalitie
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 531-555.

We study the validity of the ${L}^{p}$ inequality for the Riesz transform when $p>2$ and of its reverse inequality when $1 on complete riemannian manifolds under the doubling property and some Poincaré inequalities.

Classification : 58J35,  42B20
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title = {Riesz transform on manifolds and {Poincar\'e} inequalitie},
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Auscher, Pascal; Coulhon, Thierry. Riesz transform on manifolds and Poincaré inequalitie. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 531-555. http://archive.numdam.org/item/ASNSP_2005_5_4_3_531_0/

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