naa a22 4500 510810772 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9309-1 doi (NATIONALLICENCE)springer-10.1007/s12220-012-9309-1 Boundedness of the Hardy-Littlewood Maximal Operator Along the Orbits of Contractive Similitudes [Elektronische Daten] [Hugo Aimar, Marilina Carena, Bibiana Iaffei] 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 defined 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. Mathematica Josephina, Inc., 2012 Iterated function systems nationallicence Spaces of homogeneous nature nationallicence Hutchinson orbits nationallicence Maximal functions nationallicence Aimar Hugo Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut Carena Marilina Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut Iaffei Bibiana Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1832-1850 1050-6926 23:4<1832 2013 23 12220 https://doi.org/10.1007/s12220-012-9309-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9309-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aimar Hugo Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut NATIONALLICENCE 700 1- Carena Marilina Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut NATIONALLICENCE 700 1- Iaffei Bibiana Departamento de Matemática (FIQ-UNL), Instituto de Matemática Aplicada del Litoral (CONICET-UNL), Santa Fe, Argentina aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1832-1850 1050-6926 23:4<1832 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer