Harmonic Analysis
Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds
Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 103-108.

Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1p+, a Hardy space Hp(ΛT*M) of differential forms on M, and give two alternative characterizations of H1(ΛT*M). We also prove, for all 1p+, the Hp(ΛT*M) boundedness of Riesz transforms on M, and show that Hp(ΛT*M) has a bounded holomorphic functional calculus.

Soit M une variété riemannienne complète. Sous l'hypothèse que la mesure riemannienne est doublante, on définit, pour tout 1p+, un espace de Hardy Hp(ΛT*M) de formes différentielles sur M, et on donne deux autres caractérisations de H1(ΛT*M). On prouve également, pour tout 1p+, la continuité sur Hp(ΛT*M) des transformées de Riesz sur M, et on montre que Hp(ΛT*M) possède un calcul fonctionnel holomorphe borné.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.023
Auscher, Pascal 1; McIntosh, Alan 2; Russ, Emmanuel 3

1 CNRS UMR 8628, université Paris-sud, 91405 Orsay cedex, France
2 Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia
3 Université Paul-Cézanne LATP, avenue Escadrille Normandie-Niemen, 13397 Marseille cedex 20, France
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Auscher, Pascal; McIntosh, Alan; Russ, Emmanuel. Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds. Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 103-108. doi : 10.1016/j.crma.2006.11.023. http://www.numdam.org/articles/10.1016/j.crma.2006.11.023/

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