Boundedness of the Hardy–Littlewood Maximal Operator Along the Orbits of Contractive Similitudes

Authors
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel
Publication Year
2012
Language
English
Format
article
Status
Published version
Description
In this note we obtain results regarding the preservation of homogeneity properties along the whole orbit of a given iterated function system (IFS). We have essentially two types of results. The first class of them contains negative results: it is possible for a classical IFS to have a complete non-homogeneous sequence of spaces along the orbit, starting from very classical homogeneous spaces such as those de- fined by Muckenhoupt weights. The second class contains positive results which can be summarized here by saying that the sequence of spaces defined by the orbit of contractive similitudes starting at a normal space in the sense of Ahlfors, Macías, and Segovia, preserves doubling. As a consequence of these results we conclude boundedness properties of the Hardy–Littlewood maximal operator along the orbits.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Carena, Marilina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Iaffei, Bibiana Raquel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Subject
Iterated function systems
Spaces of homogeneous nature
Hutchinson orbits
Maximal functions
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Restricted access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/22371