Abstract

We study the density of functions which are holomorphic in a neighborhood of the closure 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×C: |w|<δ_D^α (z)},α>0,

where D⊂C and δ_D denotes distance to the boundary, is Bergman complete if and only if every boundary point of D is non-isolated. This work is joint with Prof. Bo-Yong Chen and Prof. John Erik Fornaess.