Riesz transform on manifolds and Poincaré inequalitie
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 4 (2005) no. 3, p. 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.
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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {3},
     year = {2005},
     pages = {531-555},
     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, Volume 4 (2005) no. 3, pp. 531-555. http://www.numdam.org/item/ASNSP_2005_5_4_3_531_0/

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