Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

arxiv(2024)

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摘要
We study the density of functions which are holomorphic in a neighbourhood of the closure Ω of a bounded non-smooth pseudoconvex domain Ω, in the Bergman space H^2(Ω ,φ) with a plurisubharmonic weight φ. As an application, we show that the Hartogs domain Ω _α : = {(z,w) ∈ D×: |w|< δ^α_D(z) }, α>0, where D⊂⊂ and δ_D denotes the boundary distance, is Bergman complete if and only if every boundary point of D is non-isolated.
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