A Weak Type (1,1) Estimate for a Maximal Operator on a Group of Isometries of a Homogeneous Tree

Michael Cowling; S Meda; AG Setti

doi:10.4064/cm118-1-12

A Weak Type (1,1) Estimate for a Maximal Operator on a Group of Isometries of a Homogeneous Tree

Michael Cowling, S Meda, AG Setti

Mathematics

Research output: Contribution to journal › Article

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 isometrics of the tree, and in particular for (nonabelian finitely generated) free groups.

Original language	English
Pages (from-to)	223-232
Number of pages	10
Journal	Colloquium Mathematicum
Volume	118
Issue number	1
DOIs	https://doi.org/10.4064/cm118-1-12
Publication status	Published - 1 Jan 2010

Keywords

weak type
maximal operators
homogeneous trees
convolution operators

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10.4064/cm118-1-12

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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 isometrics of the tree, and in particular for (nonabelian finitely generated) free groups.",

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AU - Setti, AG

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AB - 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 isometrics of the tree, and in particular for (nonabelian finitely generated) free groups.

KW - weak type

KW - maximal operators

KW - homogeneous trees

KW - convolution operators

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JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 1

ER -

A Weak Type (1,1) Estimate for a Maximal Operator on a Group of Isometries of a Homogeneous Tree

Abstract

Keywords

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