## Abstract

Suppose that G is a compact Lie group with finite centre. For each positive number j we consider the Ad(G)-invariant probability measure μ_{s}carried on the conjugacy class of exp(_{s}H_{p}) in G. This one-parameter family of measures is used to define a maximal function Mf, for each continuous function f on G. Our theorem states that there is an index p_{0}in (1, 2), depending on G, such that the maximal operator J? is bounded on LP(G) when p is greater than p_{0}. When the rank of G is greater than one, this provides an example of a controllable maximal operator coming from averages over a family of submanifolds, each of codimension greater than one.

Original language | English |
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Pages (from-to) | 811-822 |

Number of pages | 12 |

Journal | Transactions of the American Mathematical Society |

Volume | 315 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1989 |

Externally published | Yes |