Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L P

dc.contributor.authorFrey, Dorothee
dc.contributor.authorMcIntosh, Alan
dc.contributor.authorPortal, Pierre
dc.date.accessioned2021-07-21T00:07:48Z
dc.date.issued2018-03-07
dc.description.abstractPerturbed Hodge-Dirac operators and their holomorphic functional calculi, as investigated in the papers by Axelsson, Keith and the second author, provided insight into the solution of the Kato square-root problem for elliptic operators in L2 spaces and allowed for an extension of these estimates to other systems with applications to non-smooth boundary value problems. In this paper, we determine conditions under which such operators satisfy conical square function estimates in a range of Lp spaces, thus allowing us to apply the theory of Hardy spaces associated with an operator to prove that they have a bounded holomorphic functional calculus in those Lp spaces. We also obtain functional calculus results for restrictions to certain subspaces, for a larger range of p. This provides a framework for obtaining Lp results on perturbed Hodge Laplacians, generalising known Riesz transform bounds for an elliptic operator L with bounded measurable coefficients, one Sobolev exponent below the Hodge exponent, and Lp bounds on the square-root of L by the gradient, two Sobolev exponents below the Hodge exponent. Our proof shows that the heart of the harmonic analysis in L2 extends to Lp for all p ∈ (1,∞), while the restrictions in p come from the operator-theoretic part of the L2 proof. In the course of our work, we obtain some results of independent interest about singular integral operators on tent spaces and about the relationship between conical and vertical square functions.en_AU
dc.description.sponsorshipThe authors gratefully acknowledge support from the Australian Research Council through the Discovery Project DP120103692. This work is a key outcome of DP120103692. Frey also acknowledges support from ARC DP110102488. Portal is further supported by the ARC through the Future Fellowship FT130100607en_AU
dc.identifier.citationFrey, D., McIntosh, A. & Portal, P. Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in LP. JAMA 134, 399–453 (2018). https://doi.org/10.1007/s11854-018-0013-3en_AU
dc.identifier.issn0021-7670en_AU
dc.identifier.urihttp://hdl.handle.net/1885/241037
dc.publisherSpringeren_AU
dc.relationhttp://purl.org/au-research/grants/arc/DP110102488en_AU
dc.relationhttp://purl.org/au-research/grants/arc/DP120103692en_AU
dc.relationhttp://purl.org/au-research/grants/arc/FT130100607en_AU
dc.rights© 2018 Hebrew University Magnes Pressen_AU
dc.sourceJournal d'Analyse Mathematiqueen_AU
dc.titleConical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L Pen_AU
dc.typeJournal articleen_AU
dcterms.dateAccepted2016-02-02
local.bibliographicCitation.issue2en_AU
local.bibliographicCitation.lastpage453en_AU
local.bibliographicCitation.startpage399en_AU
local.contributor.affiliationFrey, Dorothee, College of Science, ANUen_AU
local.contributor.affiliationMcIntosh, Alan, College of Science, ANUen_AU
local.contributor.affiliationPortal, Pierre, College of Science, ANUen_AU
local.contributor.authoremailu5296569@anu.edu.auen_AU
local.contributor.authoruidFrey, Dorothee, u5296569en_AU
local.contributor.authoruidMcIntosh, Alan, u9311073en_AU
local.contributor.authoruidPortal, Pierre, u4264394en_AU
local.description.embargo2099-12-31
local.description.notesAdded manually as didn't import from ARIESen_AU
local.identifier.ariespublicationa383154xPUB9509en_AU
local.identifier.ariespublicationa383154xPUB9509
local.identifier.citationvolume134en_AU
local.identifier.doi10.1007/s11854-018-0013-3en_AU
local.identifier.uidSubmittedByu5031974en_AU
local.publisher.urlhttps://link.springer.com/en_AU
local.type.statusPublished Versionen_AU

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