A weak type $(1,1)$ estimate for a maximal operator on a group of isometries of a homogeneous tree

Volume 118 / 2010

Michael G. Cowling, Stefano Meda, Alberto G. Setti Colloquium Mathematicum 118 (2010), 223-232 MSC: Primary 43A90; Secondary 20E08, 43A85, 22E35. DOI: 10.4064/cm118-1-12


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.


  • Michael G. CowlingSchool of Mathematics
    University of Birmingham
    Edgbaston Birmingham B15 2TT, UK
  • Stefano MedaDipartimento di Matematica e Applicazioni
    Università di Milano–Bicocca
    via R. Cozzi 53
    I-20125 Milano, Italy
  • Alberto G. SettiDepartimento di Matematica e Fisica
    Università dell'Insubria
    via Valleggio 11
    I-22100 Como, Italy

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