On the Dimension of the Bergman Space of Some Hartogs Domains with Higher Dimensional Bases

On the dimension of Bergman spaces on $\mathbb{P}^1$

“…Through work of Carleson [4] and Wiegerinck [18] the dimension of the Bergman space of an open set in the complex plane is completely characterized by the polarity of the complement, see the equivalences (a)-(c) in Theorem 1.1. Wiegerinck [18] also constructs domains in C 2 whose Bergman spaces are nontrivial but finite dimensional; see [12,6,10,7,13,3] for further partial results on the dimension of Bergman spaces of open sets in higher dimensions.…”