Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

We study the density of functions which are holomorphic in a neighbourhood of the closure Ω̄ of a bounded non-smooth pseudoconvex domain Ω, in the Bergman space H²(Ω ,φ) with a plurisubharmonic weight φ. As an application, we show that the Hartogs domain Ω _α : = \(z,w) ∈ D× : |w|< δ^αD(z) \, \ \ \ α>0, where D⊂ ⊂ and δD denotes the boundary distance, is Bergman complete if and only if every boundary point of D is non-isolated.