Displaying similar documents to “On weights which admit the reproducing kernel of Bergman type.”

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 ) .

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 .

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