Local Hardy Spaces of Differential Forms on Riemannian Manifolds
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Altmetric Citations
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.author | Carbonaro, Andrea | |
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dc.contributor.author | McIntosh, Alan | |
dc.contributor.author | Morris, Andrew J. | |
dc.date.accessioned | 2015-12-22T03:13:12Z | |
dc.date.available | 2015-12-22T03:13:12Z | |
dc.identifier.issn | 1050-6926 | |
dc.identifier.uri | http://hdl.handle.net/1885/95166 | |
dc.description.abstract | 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 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.publisher | Springer Verlag | |
dc.rights | © Mathematica Josephina, Inc. 2011 | |
dc.source | Journal of Geometric Analysis | |
dc.subject | Local Hardy spaces | |
dc.subject | Riemannian manifolds | |
dc.subject | Differential forms Hodge | |
dc.subject | Dirac operators | |
dc.subject | Local Riesz transforms | |
dc.subject | Off-diagonal estimates | |
dc.title | Local Hardy Spaces of Differential Forms on Riemannian Manifolds | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 23 | |
dc.date.issued | 2011-05-24 | |
local.identifier.absfor | 010102 | |
local.identifier.absfor | 010106 | |
local.identifier.ariespublication | f2965xPUB1817 | |
local.publisher.url | http://link.springer.com/ | |
local.type.status | Published Version | |
local.contributor.affiliation | Carbonaro, Andrea, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University | |
local.contributor.affiliation | McIntosh, Alan, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University | |
local.contributor.affiliation | Morris, Andrew, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 106 | |
local.bibliographicCitation.lastpage | 169 | |
local.identifier.doi | 10.1007/s12220-011-9240-x | |
local.identifier.absseo | 970101 | |
dc.date.updated | 2016-02-24T08:17:54Z | |
local.identifier.scopusID | 2-s2.0-84872607879 | |
local.identifier.thomsonID | 000313444100006 | |
Collections | ANU Research Publications |
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