Illinois Journal of Mathematics

Bergman and Reinhardt weighted spaces of holomorphic functions

Christopher Boyd and Pilar Rueda

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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.

Article information

Illinois J. Math., Volume 49, Number 1 (2005), 217-236.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 32A36: Bergman spaces 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 46B04: Isometric theory of Banach spaces 47B38: Operators on function spaces (general)


Boyd, Christopher; Rueda, Pilar. Bergman and Reinhardt weighted spaces of holomorphic functions. Illinois J. Math. 49 (2005), no. 1, 217--236. doi:10.1215/ijm/1258138315.

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