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

David BékolléAnatole 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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