Let mu be an invariant measure on a regular orbit in a compact Lie group or in a Lie algebra. We prove sharp L(p) - L(q) estimates for the convolution operators defined through mu. We also obtain similar results for the related Radon transform on the Lie algebra
Ricci, F., Travaglini, G. (1995). L^p-L^q estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras. JOURNAL OF FUNCTIONAL ANALYSIS, 129(1), 132-147 [10.1006/jfan.1995.1045].
L^p-L^q estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras
TRAVAGLINI, GIANCARLO
1995
Abstract
Let mu be an invariant measure on a regular orbit in a compact Lie group or in a Lie algebra. We prove sharp L(p) - L(q) estimates for the convolution operators defined through mu. We also obtain similar results for the related Radon transform on the Lie algebra
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