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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Surjective isometries of weighted Bergman spaces


Author: Clinton J. Kolaski
Journal: Proc. Amer. Math. Soc. 105 (1989), 652-657
MSC: Primary 46E15; Secondary 30H05, 32F05, 32H10, 46J15
MathSciNet review: 953008
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Abstract: Let $ \Omega $ be a bounded, simply connected domain in $ {{\mathbf{C}}^n} = {R^{2n}}$, let $ F \in {L^1}({m_\Omega })$ be positive and continuo on $ \Omega $, and let $ B_F^P(\Omega ) = {L^p}(Fdm) \cap H(\Omega )(0 < p < \infty )$ denote the weighted Bergman space over $ \Omega $. We characterize those automorphisms $ \Phi $ of $ \Omega $ such that the map $ f \to g \cdot (f \circ \Phi )$ is a surjective isometry of $ B_F^P(\Omega )$, including an explicit description of $ \vert g\vert$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0953008-7
PII: S 0002-9939(1989)0953008-7
Keywords: Bergman space, isometry, automorphism
Article copyright: © Copyright 1989 American Mathematical Society