On the integral representation of superbiharmonic functions

Ali Abkar

Displaying similar documents to “On the integral representation of superbiharmonic functions”

The Bergman projection on weighted spaces: L¹ and Herz spaces

Oscar Blasco, Salvador Pérez-Esteva (2002)

Studia Mathematica

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We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces $K_{p}^{q} (w)$ .

The Bergman projection in spaces of entire functions

Jocelyn Gonessa, El Hassan Youssfi (2012)

Annales Polonici Mathematici

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We establish $L^{p}$ -estimates for the weighted Bergman projection on a nonsingular cone. We apply these results to the weighted Fock space with respect to the minimal norm in ℂⁿ.

Weighted $L^{\infty}$ -estimates for Bergman projections

José Bonet, Miroslav Engliš, Jari Taskinen (2005)

Studia Mathematica

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We consider Bergman projections and some new generalizations of them on weighted $L^{\infty} ()$ -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

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 $A^{2}$ .

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

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Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $ψ C_{ϕ}$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

On locally convex extension of $H^{\infty}$ in the unit ball and continuity of the Bergman projection

M. Jasiczak (2003)

Studia Mathematica

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We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.

On the Bergman distance on model domains in ℂⁿ

Gregor Herbort (2016)

Annales Polonici Mathematici

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Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in $ℂ^{n - 1}$ and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.

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 $i \partial \overline{\partial} φ$ .

Compact operators on the weighted Bergman space A¹(ψ)

Tao Yu (2006)

Studia Mathematica

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We show that a bounded linear operator S on the weighted Bergman space A¹(ψ) is compact and the predual space A₀(φ) of A¹(ψ) is invariant under S* if and only if $S k_{z} \to 0$ as z → ∂D, where $k_{z}$ is the normalized reproducing kernel of A¹(ψ). As an application, we give conditions for an operator in the Toeplitz algebra to be compact.

Existence of solutions to the Poisson equation in $L_{p}$ -weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_{p}$ , p≥ 3, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted L₂ space.

A Carleson inequality for $B M O A$ functions with their derivatives on the unit ball

Hasi Wulan (1998)

Commentationes Mathematicae Universitatis Carolinae

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The main purpose of this note is to give a new characterization of the well-known Carleson measure in terms of the integral for $B M O A$ functions with their derivatives on the unit ball.