Illinois Journal of Mathematics

Bergman and Reinhardt weighted spaces of holomorphic functions

Christopher Boyd and Pilar Rueda

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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.

Article information

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

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138315

Digital Object Identifier
doi:10.1215/ijm/1258138315

Mathematical Reviews number (MathSciNet)
MR2157376

Zentralblatt MATH identifier
1086.46007

Subjects
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)

Citation

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. https://projecteuclid.org/euclid.ijm/1258138315


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