Weighted Bergman projections and tangential area integrals

William Cohn

Displaying similar documents to “Weighted Bergman projections and tangential area integrals”

On the Forelli-Rudin construction and weighted Bergman projections

Ewa Ligocka (1989)

Studia Mathematica

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Holomorphic Sobolev spaces on the ball

Frank Beatrous, Jacob Burbea

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CONTENTSIntroduction ..............................................................50. Preliminaries and notation....................................61. Hilbert spaces of holomorphic functions..............112. Some estimates ..................................................163. The space $L_{q}^{p}$ ............................................224. Norm estimates...................................................305. Sobolev norms....................................................356. Projections...

Pointwise estimates for the weighted Bergman projection kernel in $ℂ^{n}$ , using a weighted $L^{2}$ estimate for the $\bar{\partial}$ equation

Henrik Delin (1998)

Annales de l'institut Fourier

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Weighted $L^{2}$ estimates are obtained for the canonical solution to the $\overline{\partial}$ equation in $L^{2} (ℂ^{n}, e^{- φ} d λ)$ , where $Ω$ is a pseudoconvex domain, and $φ$ is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in $L^{2} (ℂ^{n}, e^{- φ} d λ)$ . The weight is used to obtain a factor $e^{- ϵ ρ (z, ζ)}$ in the estimate of the kernel, where $ρ$ is the distance function in the Kähler metric given by the metric form $i \partial \overline{\partial} φ$ .

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.

On the Djrbashian kernel of a Siegel domain

Elisabetta Barletta, Sorin Dragomir (1998)

Studia Mathematica

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We establish an inversion formula for the M. M. Djrbashian A. H. Karapetyan integral transform (cf. [6]) on the Siegel domain $Ω_{n} = ζ \in ℂ^{n} : ϱ (ζ) > 0$ , $ϱ (ζ) = I m (ζ_{1}) - {| ζ^{'} |}^{2}$ . We build a family of Kähler metrics of constant holomorphic curvature whose potentials are the $ϱ^{α}$ -Bergman kernels, α > -1, (in the sense of Z. Pasternak-Winiarski [20] of $Ω_{n}$ . We build an anti-holomorphic embedding of $Ω_{n}$ in the complex projective Hilbert space $ℂ ℙ (H_{α}^{2} (Ω_{n}))$ and study (in connection with work by A. Odzijewicz [18] the corresponding transition probability...

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.

On Hardy spaces in complex ellipsoids

Thomas Hansson (1999)

Annales de l'institut Fourier

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This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space $H^{1}$ . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define $H^{1}$ with respect to a certain measure that degenerates near...

The Hölder continuity of the Bergman projection and proper holomorphic mappings

Ewa Ligocka (1984)

Studia Mathematica

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Weighted sub-Bergman Hilbert spaces in the unit disk

Ali Abkar, B. Jafarzadeh (2010)

Czechoslovak Mathematical Journal

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We study sub-Bergman Hilbert spaces in the weighted Bergman space $A_{α}^{2}$ . We generalize the results already obtained by Kehe Zhu for the standard Bergman space $A^{2}$ .