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

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

2009-04-08

arxiv.org/abs/0904.1441v1

Mathematics

Complex Variables

12 pages

Scientific paper

10.1007/s12220-010-9182-8

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.

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