Riesz transform on manifolds and Poincaré inequalitie

Auscher, Pascal¹  ; Coulhon, Thierry² 

¹ Laboratoire de Mathématiques CNRS, UMR 8628 Université de Paris-Sud 91405 Orsay Cedex, France
² Département de Mathématiques Université de Cergy-Pontoise 2 rue Adolphe Chauvin 95302 Pontoise Cedex, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 3, pp. 531-555.

Résumé

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.

Détail

Classification : 58J35, 42B20

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