A weak type $(1,1)$ estimate for a maximal operator on a group of isometries of a homogeneous tree
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 223-232
MSC: Primary 43A90; Secondary 20E08, 43A85, 22E35.
DOI: 10.4064/cm118-1-12
Abstract
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.
