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dc.contributor.authorKoskela, Pekka
dc.contributor.authorNandi, Debanjan
dc.contributor.authorNicolau, Artur
dc.date.accessioned2018-10-15T10:57:06Z
dc.date.available2018-10-15T10:57:06Z
dc.date.issued2018
dc.identifier.citationKoskela, P., Nandi, D., & Nicolau, A. (2018). Accessible parts of boundary for simply connected domains. <i>Proceedings of the American Mathematical Society</i>, <i>146</i>(8), 3403-3412. <a href="https://doi.org/10.1090/proc/13994" target="_blank">https://doi.org/10.1090/proc/13994</a>
dc.identifier.otherCONVID_28098665
dc.identifier.otherTUTKAID_77890
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/59827
dc.description.abstractFor a bounded simply connected domain Ω ⊂ R2, any point z ∈ Ω and any 0 < α < 1, we give a lower bound for the α-dimensional Hausdorff content of the set of points in the boundary of Ω which can be joined to z by a John curve with a suitable John constant depending only on α, in terms of the distance of z to ∂Ω. In fact this set in the boundary contains the intersection ∂Ωz ∩ ∂Ω of the boundary of a John subdomain Ωz of Ω, centered at z, with the boundary of Ω. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obtain the pointwise version of a weighted Hardy inequality.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesProceedings of the American Mathematical Society
dc.rightsIn Copyright
dc.subject.othersimply connected domains
dc.subject.otherJohn domains
dc.subject.otherHardy inequality
dc.titleAccessible parts of boundary for simply connected domains
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201810034325
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.date.updated2018-10-03T09:15:28Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange3403-3412
dc.relation.issn0002-9939
dc.relation.numberinseries8
dc.relation.volume146
dc.type.versionacceptedVersion
dc.rights.copyright© 2018 American Mathematical Society
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber307333 HY
dc.subject.ysoepäyhtälöt
dc.subject.ysofunktioteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p15720
jyx.subject.urihttp://www.yso.fi/onto/yso/p18494
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1090/proc/13994
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundinginformationThe third author was partially supported by the grants 2014SGR75 of Generalitat de Catalunya and MTM2014-51824-P and MTM2017-85666-P of Ministerio de Ciencia e Innovación. The first and second authors were partially supported by the Academy of Finland grant 307333.


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