Riesz transform on manifolds and Poincaré inequalitie

Auscher, Pascal; Coulhon, Thierry

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 $1<p<2$ on complete riemannian manifolds under the doubling property and some Poincaré inequalities.

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