Riesz transform on manifolds and Poincaré inequalitie

Auscher, Pascal; Coulhon, Thierry

Geodesic

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Riesz transform on manifolds and Poincaré inequalitie

Auscher, Pascal ¹ ; Coulhon, Thierry ²

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

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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.

MR Zbl

Classification : 58J35, 42B20

Affiliations des auteurs :

Auscher, Pascal ¹ ; Coulhon, Thierry ²

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     title = {Riesz transform on manifolds and {Poincar\'e} inequalitie},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {531--555},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {3},
     year = {2005},
     mrnumber = {2185868},
     zbl = {1116.58023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_3_531_0/}
}

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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://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_3_531_0/