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Hardy Spaces of Differential Forms on Riemannian Manifolds

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Auscher, Pascal; McIntosh, Alan; Russ, Emmanuel

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

dc.contributor.authorAuscher, Pascal
dc.contributor.authorMcIntosh, Alan
dc.contributor.authorRuss, Emmanuel
dc.date.accessioned2016-03-15T23:58:35Z
dc.date.available2016-03-15T23:58:35Z
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/1885/100485
dc.description.abstractLet M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces Hᴾ of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the Hᴾ -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H∞ functional calculus and Hodge decomposition, are given.
dc.publisherAmerican Mathematical Society
dc.rights© Mathematica Josephina, Inc. 2007. http://www.sherpa.ac.uk/romeo/issn/1050-6926/..." author can archive pre-print (ie pre-refereeing). Author's pre-print on pre-print servers such as arXiv.org" from SHERPA/RoMEO site (as at 22/03/16).
dc.sourceJournal of Geometric Analysis
dc.subjectRiemannian manifolds
dc.subjectHardy spaces
dc.subjectDifferential forms
dc.subjectRiesz transforms
dc.titleHardy Spaces of Differential Forms on Riemannian Manifolds
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume18
dc.date.issued2007-11-16
local.identifier.absfor010106
local.identifier.ariespublicationu4085724xPUB16
local.publisher.urlhttp://www.ams.org/journals/
local.type.statusSubmitted Version
local.contributor.affiliationAuscher, Pascal, Universite Paris-Sud, France
local.contributor.affiliationMcIntosh, Alan, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.contributor.affiliationRuss, Emmanuel, Universite Paul-Cezanne, France
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage192
local.bibliographicCitation.lastpage248
local.identifier.doi10.1007/s12220-007-9003-x
dc.date.updated2016-06-14T08:58:51Z
local.identifier.scopusID2-s2.0-84867949037
local.identifier.thomsonID000252477200008
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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