dc.creator | Molter, Úrsula María | es |
dc.creator | Rela, Ezequiel | es |
dc.date.accessioned | 2016-10-18T12:19:53Z | |
dc.date.available | 2016-10-18T12:19:53Z | |
dc.date.issued | 2013-04-15 | |
dc.identifier.citation | Molter, Ú.M. y Rela, E. (2013). Small Furstenberg sets. Journal of Mathematical Analysis and Applications, 400 (2), 475-486. | |
dc.identifier.issn | 0022-247X | es |
dc.identifier.uri | http://hdl.handle.net/11441/47712 | |
dc.description.abstract | For 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.sponsorship | Agencia Nacional de Promoción Científica y Tecnológica (Argentina) | es |
dc.description.sponsorship | Universidad de Buenos Aires | es |
dc.description.sponsorship | Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Journal of Mathematical Analysis and Applications, 400 (2), 475-486. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Furstenberg sets | es |
dc.subject | Hausdorff dimension | es |
dc.subject | Dimension function | es |
dc.subject | Jarník’s theorems | es |
dc.title | Small Furstenberg sets | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | PICT2006-00177 | es |
dc.relation.projectID | UBACyT X149 | es |
dc.relation.projectID | PIP368 | es |
dc.relation.publisherversion | http://ac.els-cdn.com/S0022247X12009055/1-s2.0-S0022247X12009055-main.pdf?_tid=b72d0526-952c-11e6-9697-00000aacb360&acdnat=1476793176_c50ef46000ead7f7c1d1e975f88f25f6 | es |
dc.identifier.doi | 10.1016/j.jmaa.2012.11.001 | es |
idus.format.extent | 17 p. | es |
dc.journaltitle | Journal of Mathematical Analysis and Applications | es |
dc.publication.volumen | 400 | es |
dc.publication.issue | 2 | es |
dc.publication.initialPage | 475 | es |
dc.publication.endPage | 486 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/47712 | |