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

ArticleOriginal scientific text

Title

Authors ¹, ¹

Department of Mathematics, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

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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