A generalization of maximal functions on compact semisimple Lie groups
type: Item
instance of: scholarly article
title: A generalization of maximal functions on compact semisimple Lie groups
zbMATH Open document ID: 0738.43001
author: Hendra Gunawan
published in: Pacific Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: Let \(G\) be a compact semisimple Lie group with finite centre. For each positive number \(s\), let \(\mu_{sH}\) denote the \(\hbox{Ad}(G)\)-invariant probability measure carried on the conjugacy class of \(\exp(sH)\) in \(G\). With this one-parameter family of measures, we define the maximal operator \({\mathcal M}_ H\) on \({\mathcal C}(G)\). Then we estimate the Fourier transform of \(\mu_{sH}\) and of some derived distributions. Our result leads to the boundedness of \({\mathcal M}_ H\) on \(L^ p(G)\), for all \(p\) greater than some index \(p_ 0\) in (1,2). This generalizes a recent result of \textit{M. Cowling} and \textit{C. Meaney} [Trans. Am. Math. Soc. 315, 811-822 (1989; Zbl 0689.42018)].
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 4216155
zbMATH Keywords: compact semisimple Lie group
zbMATH Keywords: invariant probability measure
zbMATH Keywords: one- parameter family of measures
zbMATH Keywords: maximal operator
zbMATH Keywords: Fourier transform
MaRDI profile type: Publication
full work available at URL: pjm.1992.156.119
OpenAlex ID: W2097451319
Wikidata QID: Q115230745
DOI: 10.2140/PJM.1992.156.119
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description: scientific article; zbMATH DE number 4216155