Radial limits of the Poisson kernel on the classical Cartan domains
Every -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in under a finite holomorphic map that is locally biholomorphic.
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .