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dc.creatorMolter, Úrsula Maríaes
dc.creatorRela, Ezequieles
dc.date.accessioned2016-10-18T12:19:53Z
dc.date.available2016-10-18T12:19:53Z
dc.date.issued2013-04-15
dc.identifier.citationMolter, Ú.M. y Rela, E. (2013). Small Furstenberg sets. Journal of Mathematical Analysis and Applications, 400 (2), 475-486.
dc.identifier.issn0022-247Xes
dc.identifier.urihttp://hdl.handle.net/11441/47712
dc.description.abstractFor α in (0, 1], a subset E of R2 is called Furstenberg set of type α or Fα-set if for each direction e in the unit circle there is a line segment `e in the direction of e such that the Hausdorff dimension of the set E ∩`e is greater than or equal to α. In this paper we use generalized Hausdorff measures to give estimates on the size of these sets. Our main result is to obtain a sharp dimension estimate for a whole class of zero-dimensional Furstenberg type sets. Namely, for hγ(x) = log−γ (1x), γ > 0, we construct a set Eγ ∈ Fhγ of Hausdorff dimension not greater than 1/2. Since in a previous work we showed that 1/2 is a lower bound for the Hausdorff dimension of any E ∈ Fhγ, with the present construction, the value 1/2 is sharp for the whole class of Furstenberg sets associated to the zero dimensional functions hγ.es
dc.description.sponsorshipAgencia Nacional de Promoción Científica y Tecnológica (Argentina)es
dc.description.sponsorshipUniversidad de Buenos Aireses
dc.description.sponsorshipConsejo Nacional de Investigaciones Científicas y Técnicas (Argentina)es
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofJournal of Mathematical Analysis and Applications, 400 (2), 475-486.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectFurstenberg setses
dc.subjectHausdorff dimensiones
dc.subjectDimension functiones
dc.subjectJarník’s theoremses
dc.titleSmall Furstenberg setses
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Análisis Matemáticoes
dc.relation.projectIDPICT2006-00177es
dc.relation.projectIDUBACyT X149es
dc.relation.projectIDPIP368es
dc.relation.publisherversionhttp://ac.els-cdn.com/S0022247X12009055/1-s2.0-S0022247X12009055-main.pdf?_tid=b72d0526-952c-11e6-9697-00000aacb360&acdnat=1476793176_c50ef46000ead7f7c1d1e975f88f25f6es
dc.identifier.doi10.1016/j.jmaa.2012.11.001es
idus.format.extent17 p.es
dc.journaltitleJournal of Mathematical Analysis and Applicationses
dc.publication.volumen400es
dc.publication.issue2es
dc.publication.initialPage475es
dc.publication.endPage486es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/47712

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