Journal of Lie Theory 17 (2007), No. 1, 115--144
Copyright Heldermann Verlag 2007
Lp-Boundedness of Bergman Projections in the Tube Domain over Vinberg's Cone
David Békollé
Dept. of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
dbekolle@uycdc.uninet.cm
Cyrille Nana
Dept. of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
na_cyr@yahoo.fr
We determine a range of p for which there is Lp-continuity of the Bergman projector in the tube domain over Vinberg's cone. This is the simplest example of a homogeneous non-symmetric cone. Our main tool is the existence of a suitable isometry between the cone and its dual.
Keywords: Bergman spaces, Bergman projections, homogeneous cones, interpolation.
MSC: 32A20, 32A10, 32A25, 32A36
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