التفاصيل البيبلوغرافية
| العنوان: |
Small Furstenberg sets |
| المؤلفون: |
Molter, Úrsula María, Rela, Ezequiel |
| المساهمون: |
Universidad de Sevilla. Departamento de Análisis Matemático |
| بيانات النشر: |
Elsevier |
| سنة النشر: |
2016 |
| المجموعة: |
idUS - Deposito de Investigación Universidad de Sevilla |
| مصطلحات موضوعية: |
Furstenberg sets, Hausdorff dimension, Dimension function, Jarník’s theorems |
| الوصف: |
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. ; Agencia Nacional de Promoción Científica y Tecnológica (Argentina) ; Universidad de Buenos Aires ; Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) |
| نوع الوثيقة: |
article in journal/newspaper |
| اللغة: |
English |
| Relation: |
Journal of Mathematical Analysis and Applications, 400 (2), 475-486.; PICT2006-00177; UBACyT X149; PIP368; http://ac.els-cdn.com/S0022247X12009055/1-s2.0-S0022247X12009055-main.pdf?_tid=b72d0526-952c-11e6-9697-00000aacb360&acdnat=1476793176_c50ef46000ead7f7c1d1e975f88f25f6; https://idus.us.es/handle/11441/47712 |
| الاتاحة: |
https://idus.us.es/handle/11441/47712 |
| Rights: |
Attribution-NonCommercial-NoDerivatives 4.0 Internacional ; http://creativecommons.org/licenses/by-nc-nd/4.0/ ; info:eu-repo/semantics/openAccess |
| رقم الانضمام: |
edsbas.E0A5EC82 |
| قاعدة البيانات: |
BASE |