Journal of Lie Theory 21 (2011), No. 3, 499--613
Copyright Heldermann Verlag 2011
Boundedness of the Cauchy Harish-Chandra Integral
Florent Bernon
Dép. de Mathématiques, Université de Versailles, 78035 Versailles, France
Florent.Bernon@math.uvsq.fr
Tomasz Przebinda
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
tprzebinda@gmail.com
This is the first of our three articles showing that the Cauchy Harish-Chandra integral maps invariant eigendistributions to invariant eigendistributions with the correct infinitesimal character. Here we prove that all the derivatives of the Cauchy Harish-Chandra integral are bounded.
Keywords: Dual pairs, orbital integrals.
MSC: 22E45; 22E46
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