Reproducing properties and $L^p$-estimates for Bergman projections in Siegel domains of type II
Volume 115 / 1995
Studia Mathematica 115 (1995), 219-239
DOI: 10.4064/sm-115-3-219-239
Abstract
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted $L^p$-space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some $L^p$-estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space $A^2$.
