Displaying similar documents to “Weighted generalization of the Ramadanov's theorem and further considerations”

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.

Commutant of multiplication operators in weighted Bergman spaces on polydisk

Ali Abkar (2020)

Czechoslovak Mathematical Journal

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We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the n -dimensional complex plane. Characterization of the commutant of such operators is given.

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

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.

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 ) .

Weighted sub-Bergman Hilbert spaces

Maria Nowak, Renata Rososzczuk (2014)

Annales UMCS, Mathematica

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We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers

Traces of functions in Bergman weighted spaces on tubular domains

Umberto Sampieri (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dà una caratterizzazione completa per tracce di funzioni olomorfe a quadrato sommabile per particolari misure su domini tubolari.

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 ) ∈ 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.

Weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type space

Elke Wolf (2009)

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 Banach spaces of holomorphic functions and weighted Bloch type spaces. Under some assumptions on the weights we give a necessary as well as a sufficient condition for such an operator to be bounded resp. compact.

On the weighted estimate of the Bergman projection

Benoît Florent Sehba (2018)

Czechoslovak Mathematical Journal

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We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.

Pointwise estimates for the weighted Bergman projection kernel in ℂ n , using a weighted L 2 estimate for the ∂ ¯ 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 ∂ ‾ 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 ∂ ∂ ‾ φ .

On some extremal problems in Bergman spaces in weakly pseudoconvex domains

Romi F. Shamoyan, Olivera R. Mihić (2018)

Communications in Mathematics

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We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂ n based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces A α p in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.