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Transactions of the American Mathematical Society

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



Bounded point evaluation in $\textbf {C}^ n$

Authors: R. M. Range and M. I. Stessin
Journal: Trans. Amer. Math. Soc. 347 (1995), 2169-2177
MSC: Primary 32A37; Secondary 46E22
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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Keywords: Bounded point evaluation, reproducing kernel, Bergman spaces
Article copyright: © Copyright 1995 American Mathematical Society