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Displaying similar documents to “Three related problems of Bergman spaces of tube domains over symmetric cones”

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

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Let Ω be a bounded strictly pseudoconvex domain in ℂ n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) .

Hölder functions in Bergman type spaces

Yingwei Chen, Guangbin Ren (2012)

Studia Mathematica

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It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth...

Bergman function, Genchev transform and L²-angles, for multidimensional tubes

Hyb Wojciech

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CONTENTS1. Introduction.......................................................................................................52. Basic definitions, notations and facts................................................................63. Definitions of the Genchev transform................................................................84. Basic properties of the Genchev transform......................................................115. Some properties of the weight w B ..............................................................166....

On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

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In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic...

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 .

The Bergman kernel functions of certain unbounded domains

Friedrich Haslinger (1998)

Annales Polonici Mathematici

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We compute the Bergman kernel functions of the unbounded domains Ω p = ( z ' , z ) ∈ ℂ ² : z > p ( z ' ) , where p ( z ' ) = | z ' | α / α . It is also shown that these kernel functions have no zeros in Ω p . We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.