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Pré-Publication, Document De Travail Année : 2019

Hardy spaces on Riemannian manifolds with quadratic curvature decay

Baptiste Devyver
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Emmanuel Russ

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.
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Dates et versions

hal-02320652 , version 1 (19-10-2019)
hal-02320652 , version 2 (09-11-2020)

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Baptiste Devyver, Emmanuel Russ. Hardy spaces on Riemannian manifolds with quadratic curvature decay. 2019. ⟨hal-02320652v1⟩
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