Tokyo Journal of Mathematics

On a Weak $L^1$ Property of Maximal Operators on Non-Compact Semisimple Lie Groups

Takeshi KAWAZOE and Jianming LIU

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We shall give a simple proof of the weak type $L^1$ inequality for the $K$-bi-invariant Hardy-Littlewood maximal functions on non-compact real rank one semisimple Lie groups. For higher rank groups we do under an assumption which holds for the most parts. And on $SU(n,n+k)$ we introduce a maximal operator defined by the characteristic function supported on a cube, and show that the operator also satisfies the weak $L^1$ property.

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Tokyo J. Math., Volume 25, Number 1 (2002), 165-180.

First available in Project Euclid: 5 June 2009

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KAWAZOE, Takeshi; LIU, Jianming. On a Weak $L^1$ Property of Maximal Operators on Non-Compact Semisimple Lie Groups. Tokyo J. Math. 25 (2002), no. 1, 165--180. doi:10.3836/tjm/1244208943.

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