Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds

Pascal Auscher; Alan McIntosh; Emmanuel Russ

doi:10.1016/j.crma.2006.11.023

Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds

Pascal Auscher^*, Alan McIntosh, Emmanuel Russ

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1 ≤ p ≤ + ∞, a Hardy space H^p (Λ T^* M) of differential forms on M, and give two alternative characterizations of H¹ (Λ T^* M). We also prove, for all 1 ≤ p ≤ + ∞, the H^p (Λ T^* M) boundedness of Riesz transforms on M, and show that H^p (Λ T^* M) has a bounded holomorphic functional calculus. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

Original language	English
Pages (from-to)	103-108
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	344
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2006.11.023
Publication status	Published - 15 Jan 2007

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abstract = "Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1 ≤ p ≤ + ∞, a Hardy space Hp (Λ T* M) of differential forms on M, and give two alternative characterizations of H1 (Λ T* M). We also prove, for all 1 ≤ p ≤ + ∞, the Hp (Λ T* M) boundedness of Riesz transforms on M, and show that Hp (Λ T* M) has a bounded holomorphic functional calculus. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).",

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AU - Russ, Emmanuel

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N2 - Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1 ≤ p ≤ + ∞, a Hardy space Hp (Λ T* M) of differential forms on M, and give two alternative characterizations of H1 (Λ T* M). We also prove, for all 1 ≤ p ≤ + ∞, the Hp (Λ T* M) boundedness of Riesz transforms on M, and show that Hp (Λ T* M) has a bounded holomorphic functional calculus. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

AB - Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1 ≤ p ≤ + ∞, a Hardy space Hp (Λ T* M) of differential forms on M, and give two alternative characterizations of H1 (Λ T* M). We also prove, for all 1 ≤ p ≤ + ∞, the Hp (Λ T* M) boundedness of Riesz transforms on M, and show that Hp (Λ T* M) has a bounded holomorphic functional calculus. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

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Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds

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