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dc.contributor.authorCoulhon, Thierry
dc.contributor.authorJiang, Renjin
dc.contributor.authorKoskela, Pekka
dc.contributor.authorSikora, Adam
dc.date.accessioned2020-01-31T09:59:34Z
dc.date.available2020-01-31T09:59:34Z
dc.date.issued2020
dc.identifier.citationCoulhon, T., Jiang, R., Koskela, P., & Sikora, A. (2020). Gradient estimates for heat kernels and harmonic functions. <i>Journal of Functional Analysis</i>, <i>278</i>(8), Article 108398. <a href="https://doi.org/10.1016/j.jfa.2019.108398" target="_blank">https://doi.org/10.1016/j.jfa.2019.108398</a>
dc.identifier.otherCONVID_33599622
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/67655
dc.description.abstractLet (X,d,μ) be a doubling metric measure space endowed with a Dirichlet form E deriving from a “carré du champ”. Assume that (X,d,μ,E) supports a scale-invariant L2-Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for p∈(2,∞]: (i) (Gp): Lp-estimate for the gradient of the associated heat semigroup; (ii) (RHp): Lp-reverse Hölder inequality for the gradients of harmonic functions; (iii) (Rp): Lp-boundedness of the Riesz transform (p<∞); (iv) (GBE): a generalised Bakry-Émery condition. We show that, for p∈(2,∞), (i), (ii) (iii) are equivalent, while for p=∞, (i), (ii), (iv) are equivalent. Moreover, some of these equivalences still hold under weaker conditions than the L2-Poincaré inequality. Our result gives a characterisation of Li-Yau's gradient estimate of heat kernels for p=∞, while for p∈(2,∞) it is a substantial improvement as well as a generalisation of earlier results by Auscher-Coulhon-Duong-Hofmann [7] and Auscher-Coulhon [6]. Applications to isoperimetric inequalities and Sobolev inequalities are given. Our results apply to Riemannian and sub-Riemannian manifolds as well as to non-smooth spaces, and to degenerate elliptic/parabolic equations in these settings.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesJournal of Functional Analysis
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherharmonic functions
dc.subject.otherheat kernels
dc.subject.otherLi-Yau estimates
dc.subject.otherRiesz transform
dc.titleGradient estimates for heat kernels and harmonic functions
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202001311920
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0022-1236
dc.relation.numberinseries8
dc.relation.volume278
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 Elsevier Inc.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber307333 HY
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysoharmoninen analyysi
dc.subject.ysodifferentiaaligeometria
dc.subject.ysopotentiaaliteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p28124
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
jyx.subject.urihttp://www.yso.fi/onto/yso/p18911
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1016/j.jfa.2019.108398
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundinginformationT. Coulhon and A. Sikora were partially supported by Australian Research Council Discovery grant DP130101302. This research was undertaken while T. Coulhon was employed by the Australian National University. R. Jiang was partially supported by NNSF of China (11922114 & 11671039), P. Koskela was partially supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (project No. 307333).
dc.type.okmA1


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