A Remark on the Dimension of the Bergman Space of Some Hartogs Domains

作者：Jucha Piotr^*

来源：Journal of Geometric Analysis, 2012, 22(1): 23-37.

DOI：10.1007/s12220-010-9182-8

• Bergman spaces
• Hartogs domains
• Subharmonic functions

Let D be a Hartogs domain of the form D = {(z, w). C x C-N : parallel to w parallel to %26lt; 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.

• 出版日期2012-1