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
@article{ASNSP_2005_5_4_3_531_0,
author = {Auscher, Pascal and Coulhon, Thierry},
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},
zbl = {1116.58023},
mrnumber = {2185868},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2005_5_4_3_531_0/}
}
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://www.numdam.org/item/ASNSP_2005_5_4_3_531_0/

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