On the Wu metric in unbounded domains

We discuss the properties of the Wu pseudometric and present counterexamples for its upper semicontinuity that answers the question posed by Jarnicki and Pflug. We also give formulae for the Wu pseudometric in elementary Reinhardt domains.Comment: 11 page

A remark on the dimension of the Bergman space of some Hartogs domains

Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite dimensional.Comment: 12 page

Społeczno-ekonomiczne i przestrzenne przemiany struktur regionalnych Vol. 2

Praca recenzowana / peer-reviewed pape