Displaying similar documents to “Supplement to “Some remarks on Poincaré series””

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

David Békollé, Anatole Temgoua Kagou (1995)

Studia Mathematica

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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 .

Interpolating varieties for weighted spaces of entire functions in C.

Carlos A. Berenstein, Qin Li Bao (1994)

Publicacions Matemàtiques

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We prove in this paper that a given discrete variety V in C is an interpolating variety for a weight p if and only if V is a subset of the variety {ξ ∈ C: f(ξ) = f(ξ) = ... = f(ξ) = 0} of m functions f, ..., f in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-C(ζ)), ζ ∈ V for some constants ε, C &gt; 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f, ..., f. As a corollary, we...