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 journalArticlepeer-review

    5 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 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).

    Original languageEnglish
    Pages (from-to)103-108
    Number of pages6
    JournalComptes Rendus Mathematique
    Volume344
    Issue number2
    DOIs
    Publication statusPublished - 15 Jan 2007

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