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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

Tomasz Przebinda
Dept. of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.

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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