Hardy spaces on Riemannian manifolds with quadratic curvature decay
Résumé
Let (M, g) be a complete Riemannian manifold. Assume that the Ricci curvature of M has quadratic decay and that the volume growth is strictly faster than quadratic. We establish that the Hardy spaces of exact 1-differential forms on M , introduced in [4], coincide with the closure in L p of R(d) ∩ L p (Λ 1 T * M) when 1 < p < ν, where ν > 2 is related to the volume growth. The range of p is optimal. This result applies, in particular, when M has a finite number of Euclidean ends.
Domaines
Analyse classique [math.CA]Origine | Fichiers produits par l'(les) auteur(s) |
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