Bergman and Reinhardt weighted spaces of holomorphic functions

Abstract

We study isometries between spaces of weighted holomorphic functions defined on bounded domains in $\mathbf{C}^n$. Using the Bergman kernel we see that it is possible to define a `natural' weight on bounded domains in $\mathbf{C}^n$. We calculate the isometries of weighted spaces of holomorphic functions on the unit ball, the Thullen domains, the generalised Thullen domains and the domain with minimal complex norm.