Show simple item record

dc.contributor.authorHofmann, Steve
dc.contributor.authorTapiola, Olli
dc.date.accessioned2021-06-14T12:08:48Z
dc.date.available2021-06-14T12:08:48Z
dc.date.issued2020
dc.identifier.citationHofmann, S., & Tapiola, O. (2020). Uniform rectifiability and ε-approximability of harmonic functions in Lp. <i>Annales de l'Institut Fourier</i>, <i>70</i>(4), 1595-1638. <a href="https://doi.org/10.5802/aif.3359" target="_blank">https://doi.org/10.5802/aif.3359</a>
dc.identifier.otherCONVID_97818425
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/76515
dc.description.abstractSuppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that pointwise, L∞ and Lp type ε-approximability properties of harmonic functions are all equivalent and they characterize uniform rectifiability for codimension 1 Ahlfors–David regular sets. Our results and techniques are generalizations of recent works of T. Hytönen and A. Rosén and the first author, J. M. Martell and S. Mayboroda.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherCentre Mersenne; l'Institut Fourier,
dc.relation.ispartofseriesAnnales de l'Institut Fourier
dc.rightsCC BY-ND 4.0
dc.subject.otherε-approximability
dc.subject.otheruniform rectifiability
dc.subject.otherCarleson measures
dc.subject.otherharmonic functions.
dc.titleUniform rectifiability and ε-approximability of harmonic functions in Lp
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202106143717
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineAnalyysin ja dynamiikan tutkimuksen huippuyksikköfi
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineAnalysis and Dynamics Research (Centre of Excellence)en
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1595-1638
dc.relation.issn0373-0956
dc.relation.numberinseries4
dc.relation.volume70
dc.type.versionpublishedVersion
dc.rights.copyright© 2020 Association des Annales de l’institut Fourier
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber307333 HY
dc.subject.ysoharmoninen analyysi
dc.subject.ysomittateoria
dc.subject.ysopotentiaaliteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p28124
jyx.subject.urihttp://www.yso.fi/onto/yso/p13386
jyx.subject.urihttp://www.yso.fi/onto/yso/p18911
dc.rights.urlhttps://creativecommons.org/licenses/by-nd/4.0/
dc.relation.doi10.5802/aif.3359
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundinginformationS.H. was supported by NSF grant DMS-1664047. O.T. was supported by Emil Aaltosen Säätiö through Foundations’ Post Doc Pool grant. In the previous stages of this work, he was supported by the European Union through T. Hytönen’s ERC Starting Grant 278558 “Analytic-probabilistic methods for borderline singular integrals” and the Finnish Centre of Excellence in Analysis and Dynamics Research.


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

CC BY-ND 4.0
Except where otherwise noted, this item's license is described as CC BY-ND 4.0