Characterization of the Poisson integrals for the non-tube bounded symmetric domains
The main result states that the \(L^p\)-range (\(p>1\)) of the Poisson transform on the Shilov boundary for non-tube bounded symmetric domains \(\Omega\) is a Hardy type space for the solutions of a Hua system, which are eigenfunctions of all invariant differential operators on \(\Omega\). The method of proof follows the one used in [\textit{S.Ben Said, T. Oshima} and \textit{N. Shimeno}, Int. Math. Res. Not. 2003, No.~16, 915--931 (2003; Zbl 1020.43005)], which in turn is similar to the one given in [\textit{M. Stoll}, J.~Reine Angew. Math. 271, 63--76 (1974; Zbl 0298.43017)] in the harmonic case. The crucial point is the reduction to the case \(p=2\).
scientific article; zbMATH DE number 5148781
scientific article