Hardy spaces of differential forms on riemannian manifolds

Pascal Auscher; Alan McIntosh; Emmanuel Russ

doi:10.1007/s12220-007-9003-x

Hardy spaces of differential forms on riemannian manifolds

Pascal Auscher^*, Alan McIntosh, Emmanuel Russ

^*Corresponding author for this work

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

159 Citations (Scopus)

Abstract

Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H ^p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H ^p -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H ^∞ functional calculus and Hodge decomposition, are given.

Original language	English
Pages (from-to)	192-248
Number of pages	57
Journal	Journal of Geometric Analysis
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s12220-007-9003-x
Publication status	Published - Jan 2008

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title = "Hardy spaces of differential forms on riemannian manifolds",

abstract = "Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H p -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H ∞ functional calculus and Hodge decomposition, are given.",

keywords = "Differential forms, Hardy spaces, Riemannian manifolds, Riesz transforms",

author = "Pascal Auscher and Alan McIntosh and Emmanuel Russ",

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AU - Auscher, Pascal

AU - McIntosh, Alan

AU - Russ, Emmanuel

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N2 - Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H p -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H ∞ functional calculus and Hodge decomposition, are given.

AB - Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H p -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H ∞ functional calculus and Hodge decomposition, are given.

KW - Differential forms

KW - Hardy spaces

KW - Riemannian manifolds

KW - Riesz transforms

UR - https://www.scopus.com/pages/publications/84867949037

U2 - 10.1007/s12220-007-9003-x

DO - 10.1007/s12220-007-9003-x

M3 - Article

SN - 1050-6926

VL - 18

SP - 192

EP - 248

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

ER -

Hardy spaces of differential forms on riemannian manifolds

Abstract

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