On the Forelli-Rudin construction and weighted Bergman projections

Ewa Ligocka

Displaying similar documents to “On the Forelli-Rudin construction and weighted Bergman projections”

The Hölder continuity of the Bergman projection and proper holomorphic mappings

Ewa Ligocka (1984)

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Remarks on the Bergman kernel function of a worm domain

Ewa Ligocka (1998)

Studia Mathematica

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We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be $C^{\infty}$ -smoothly extended to the boundary.

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 $H_{k}^{p} (\partial Ω)$ . 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 $H_{k}^{p} (\partial Ω)$ .

Some applications of the Bergman kernel to geometrical theory of functions

I. Ramadanov (1983)

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Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in $𝐂^{2}$

Joe Kamimoto (1998)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Duality theorems for Hardy and Bergman spaces on convex domains of finite type in $ℂ^{n}$

Steven G. Krantz, Song-Ying Li (1995)

Annales de l'institut Fourier

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We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in $n$ -dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.

Bergman completeness of Zalcman type domains

Piotr Jucha (2004)

Studia Mathematica

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We give an equivalent condition for Bergman completeness of Zalcman type domains. This also solves a problem stated by Pflug.

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 $Ω_{p} = (z^{'}, z) \in ℂ ² : z > p (z^{'})$ , 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.

The Bergman kernel of the minimal ball and applications

Karl Oeljeklaus, Peter Pflug, El Hassan Youssfi (1997)

Annales de l'institut Fourier

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In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in $ℂ^{n}$ that extends the euclidean norm in $ℝ^{n}$ and give some applications.