On a maximal function on compact lie groups

Michael Cowling, Christopher Meaney

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 μscarried on the conjugacy class of exp(sHp) 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 p0in (1, 2), depending on G, such that the maximal operator J? is bounded on LP(G) when p is greater than p0. 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 languageEnglish
Pages (from-to)811-822
Number of pages12
JournalTransactions of the American Mathematical Society
Volume315
Issue number2
DOIs
Publication statusPublished - 1989
Externally publishedYes

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