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Reproducing properties and $L^{p}$ -estimates for Bergman projections in Siegel domains of type II

David Békollé; Anatole Temgoua Kagou — 1995

Studia Mathematica

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 $A^{2}$ .

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Reproducing properties and L p -estimates for Bergman projections in Siegel domains of type II

Reproducing properties and $L^{p}$ -estimates for Bergman projections in Siegel domains of type II