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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bounded point evaluation in $ {\bf C}\sp n$


Authors: R. M. Range and M. I. Stessin
Journal: Trans. Amer. Math. Soc. 347 (1995), 2169-2177
MSC: Primary 32A37; Secondary 46E22
DOI: https://doi.org/10.1090/S0002-9947-1995-1254851-7
MathSciNet review: 1254851
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Abstract: A positive Borel measure $ \mu $ on a domain $ \Omega \in {{\mathbf{C}}^n}$ is said to be in $ \mathcal{R}(\Omega )$, if point evaluations at every $ p \in \Omega $ are locally uniformly bounded in $ {L^2}(\mu )$-norm. It is proved that the multiplication of a measure in $ \mathcal{R}(\Omega )$ by a function decreasing no faster than a power of a holomorphic function produces a measure in $ \mathcal{R}(\Omega )$. Some applications to classical Hardy and Bergman spaces are given.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1254851-7
Keywords: Bounded point evaluation, reproducing kernel, Bergman spaces
Article copyright: © Copyright 1995 American Mathematical Society