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

Abstract

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.

arXiv comment12 pages

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