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A generalization of
maximal functions on compact semisimple Lie groups
Hendra Gunawan |
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Vol. 156 (1992), No. 1, 119–134
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Abstract |
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Let G be a compact semisimple Lie group with finite centre. For each positive number s, let μsH denote the 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 ℳH on 𝒞(G). We then estimate the Fourier transform of μsH and of some derived distributions. Our result leads to the boundedness of ℳH on Lp(G), for all p greater than some index p0 in (1,2). This generalizes a recent result of M. Cowling and C. Meaney [2]. |
Mathematical Subject Classification 2000
Primary: 22E30
Secondary: 42B25, 43A15
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Milestones
Received: 21 March 1991
Revised: 16 October 1991
Published: 1 November 1992
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Authors |
| Hendra Gunawan | |
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