Artículo
Boundedness of the Hardy–Littlewood Maximal Operator Along the Orbits of Contractive Similitudes
Fecha de publicación:
03/2012
Editorial:
Springer
Revista:
The Journal Of Geometric Analysis
ISSN:
1050-6926
e-ISSN:
1559-002X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Articulos(IMAL)
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Citación
Aimar, Hugo Alejandro; Carena, Marilina; Iaffei, Bibiana Raquel; Boundedness of the Hardy–Littlewood Maximal Operator Along the Orbits of Contractive Similitudes; Springer; The Journal Of Geometric Analysis; 23; 4; 3-2012; 1832-1850
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