Bounded pluriharmonic functions on symmetric irreducible Siegel domains
Let \(\mathcal D\) be an irreducible symmetric Siegel domain and let \(S\) be a solvable group which acts transitively on \(\mathcal D\). The authors define three \(S\)-invariant second order degenerate elliptic operators \textbf{L}, \(\mathcal L\), \textbf{H} such that a bounded function \(F\) on \(\mathcal D\) is pluriharmonic iff \textbf{L}\(F=\mathcal LF= \)\textbf{H}\(F=0\). The results extend a former paper by \textit{E. Damek, A. Hulanicki, D. Müller} and \textit{M. Peloso} [Geom. Funct. Anal. 10, No. 5, 1090-1117 (2000; Zbl 0969.31007)].
scientific article; zbMATH DE number 1801583