dc.creator | Molter, Úrsula María | es |
dc.creator | Rela, Ezequiel | es |
dc.date.accessioned | 2016-10-19T06:08:39Z | |
dc.date.available | 2016-10-19T06:08:39Z | |
dc.date.issued | 2012-08 | |
dc.identifier.citation | Molter, Ú.M. y Rela, E. (2012). Furstenberg sets for a fractal set of directions. Proceedings of the American Mathematical Society, 140 (8), 2753-2765. | |
dc.identifier.issn | 0002-9939 | es |
dc.identifier.issn | 1088-6826 | es |
dc.identifier.uri | http://hdl.handle.net/11441/47719 | |
dc.description.abstract | In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the set of directions defining it. For any pair α, β ∈ (0, 1], we will say that a set E ⊂ R2 is an Fαβ-set if there is a subset L of the unit circle of Hausdorff dimension at least β and, for each direction e in L, there is a line segment e in the direction of e such that the Hausdorff dimension
of the set E∩ e is equal to or greater than α. The problem is considered in
the wider scenario of generalized Hausdorff measures, giving estimates on the appropriate dimension functions for each class of Furstenberg sets. As a corollary of our main results, we obtain that dim(E) ≥ max {α + β 2 ; 2α + β − 1} for any E ∈ Fαβ. In particular we are able to extend previously known results to the “endpoint” α = 0 case. | es |
dc.description.sponsorship | Agencia Nacional de Promoción Científica y Tecnológica (Argentina) | es |
dc.description.sponsorship | Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) | es |
dc.description.sponsorship | Universidad de Buenos Aires | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | American Mathematical Society | es |
dc.relation.ispartof | Proceedings of the American Mathematical Society, 140 (8), 2753-2765. | |
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 | Kakeya sets | es |
dc.title | Furstenberg sets for a fractal set of directions | es |
dc.type | info:eu-repo/semantics/article | es |
dc.type.version | info:eu-repo/semantics/acceptedVersion | 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 | PIP 11220080100398 | es |
dc.relation.projectID | UBACyT X149 | es |
dc.relation.publisherversion | https://doi.org/10.1090/S0002-9939-2011-11111-0 | es |
dc.identifier.doi | 10.1090/S0002-9939-2011-11111-0 | es |
idus.format.extent | 13 p. | es |
dc.journaltitle | Proceedings of the American Mathematical Society | es |
dc.publication.volumen | 140 | es |
dc.publication.issue | 8 | es |
dc.publication.initialPage | 2753 | es |
dc.publication.endPage | 2765 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/47719 | |