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Local Hardy Spaces of Differential Forms on Riemannian Manifolds

Carbonaro, Andrea; McIntosh, Alan; Morris, Andrew J.

Description

We define local Hardy spaces of differential forms hDᴾ(∧T∗M) for all p∈[1,∞] that are adapted to a class of first-order differential operators D on a complete Riemannian manifold M with at most exponential volume growth. In particular, if D is the Hodge–Dirac operator on M and Δ=D² is the Hodge–Laplacian, then the local geometric Riesz transform D(Δ+aI)⁻¹/² has a bounded extension to hDᴾ for all p∈[1,∞], provided that a>0 is large enough compared to the exponential growth of M. A...[Show more]

dc.contributor.authorCarbonaro, Andrea
dc.contributor.authorMcIntosh, Alan
dc.contributor.authorMorris, Andrew J.
dc.date.accessioned2015-12-22T03:13:12Z
dc.date.available2015-12-22T03:13:12Z
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/1885/95166
dc.description.abstractWe define local Hardy spaces of differential forms hDᴾ(∧T∗M) for all p∈[1,∞] that are adapted to a class of first-order differential operators D on a complete Riemannian manifold M with at most exponential volume growth. In particular, if D is the Hodge–Dirac operator on M and Δ=D² is the Hodge–Laplacian, then the local geometric Riesz transform D(Δ+aI)⁻¹/² has a bounded extension to hDᴾ for all p∈[1,∞], provided that a>0 is large enough compared to the exponential growth of M. A characterization of h1D in terms of local molecules is also obtained. These results can be viewed as the localization of those for the Hardy spaces of differential forms HDᴾ(∧T∗M) introduced by Auscher, McIntosh, and Russ
dc.publisherSpringer Verlag
dc.rights© Mathematica Josephina, Inc. 2011
dc.sourceJournal of Geometric Analysis
dc.subjectLocal Hardy spaces
dc.subjectRiemannian manifolds
dc.subjectDifferential forms Hodge
dc.subjectDirac operators
dc.subjectLocal Riesz transforms
dc.subjectOff-diagonal estimates
dc.titleLocal Hardy Spaces of Differential Forms on Riemannian Manifolds
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume23
dc.date.issued2011-05-24
local.identifier.absfor010102
local.identifier.absfor010106
local.identifier.ariespublicationf2965xPUB1817
local.publisher.urlhttp://link.springer.com/
local.type.statusPublished Version
local.contributor.affiliationCarbonaro, Andrea, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
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.affiliationMorris, Andrew, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage106
local.bibliographicCitation.lastpage169
local.identifier.doi10.1007/s12220-011-9240-x
local.identifier.absseo970101
dc.date.updated2016-02-24T08:17:54Z
local.identifier.scopusID2-s2.0-84872607879
local.identifier.thomsonID000313444100006
CollectionsANU Research Publications

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