98-4   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Ewa Damek, Andrzej Hulanicki, Marco M. Peloso, Detlef Müller:

Pluriharmonic H 2 functions on symmetric irreducible Siegel domains

Let D be a homogeneous bounded domain in Cm. Pluriharmonic functions, i.e. real parts of holomorphic functions, are characterized locally by the equations
\partial _{z_j}\partial _{\ov{z}_k}F=0,\ \ j, k=1,\dots, m.
Another system which characterizes pluriharmonicity is the system of one-dimensional laplacians along m2 appropriately chosen one-dimensional complex subspaces, a system of degenerate elliptic, real operators. The aim of this paper is to show that for domains which exhibit lots of symmetries, the number of degenerate elliptic operators needed to yield such a characterization can drastically be reduced. More precisely, if the domain D is symmetric and irreducible, then only three such operators are needed, in general, and if in addition D is of tube type, even two suffice, provided that the functions under consideration satisfy an H2 growth condition.

Mathematics Subject Classification (1991): 32M15, sowie 22E25, 31B25, 43A85

Bibliographical note: erscheint Geom. and Funct. Anal.

Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]
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