Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all , a Hardy space of differential forms on M, and give two alternative characterizations of . We also prove, for all , the boundedness of Riesz transforms on M, and show that 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 , un espace de Hardy de formes différentielles sur M, et on donne deux autres caractérisations de . On prouve également, pour tout , la continuité sur des transformées de Riesz sur M, et on montre que possède un calcul fonctionnel holomorphe borné.
Accepted:
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Pascal Auscher 1; Alan McIntosh 2; Emmanuel Russ 3
@article{CRMATH_2007__344_2_103_0, author = {Pascal Auscher and Alan McIntosh and Emmanuel Russ}, title = {Hardy spaces of differential forms and {Riesz} transforms on {Riemannian} manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {103--108}, publisher = {Elsevier}, volume = {344}, number = {2}, year = {2007}, doi = {10.1016/j.crma.2006.11.023}, language = {en}, }
TY - JOUR AU - Pascal Auscher AU - Alan McIntosh AU - Emmanuel Russ TI - Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds JO - Comptes Rendus. Mathématique PY - 2007 SP - 103 EP - 108 VL - 344 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2006.11.023 LA - en ID - CRMATH_2007__344_2_103_0 ER -
Pascal Auscher; Alan McIntosh; Emmanuel Russ. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.023/
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