Geodesic
A weak type $(1,1)$ estimate for a maximal operator on a group of isometries of a homogeneous tree
Michael G. Cowling 1   ; Stefano Meda 2   ; Alberto G. Setti 3
1 School of Mathematics University of Birmingham Edgbaston Birmingham B15 2TT, UK
2 Dipartimento di Matematica e Applicazioni Università di Milano–Bicocca via R. Cozzi 53 I-20125 Milano, Italy
3 Departimento di Matematica e Fisica Università dell'Insubria via Valleggio 11 I-22100 Como, Italy
Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 223-232 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy–Littlewood and spherical maximal operators, are of weak type $(1,1)$. This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.
DOI : 10.4064/cm118-1-12
Keywords: simple proof result rochberg taibleson various maximal operators homogeneous tree including hardy littlewood spherical maximal operators weak type result extends corresponding maximal operators transitive group isometries tree particular nonabelian finitely generated groups

Michael G. Cowling  1   ; Stefano Meda  2   ; Alberto G. Setti  3

1 School of Mathematics University of Birmingham Edgbaston Birmingham B15 2TT, UK
2 Dipartimento di Matematica e Applicazioni Università di Milano–Bicocca via R. Cozzi 53 I-20125 Milano, Italy
3 Departimento di Matematica e Fisica Università dell'Insubria via Valleggio 11 I-22100 Como, Italy 
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Michael G. Cowling; Stefano Meda; Alberto G. Setti. A weak type $(1,1)$ estimate for a maximal operator
 on a group of isometries of a homogeneous tree. Colloquium Mathematicum, Tome 118 (2010) no. 1, pp. 223-232. doi: 10.4064/cm118-1-12

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