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Transactions of the American Mathematical Society

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

 

 

Existence domains of holomorphic functions of restricted growth


Authors: M. Jarnicki and P. Pflug
Journal: Trans. Amer. Math. Soc. 304 (1987), 385-404
MSC: Primary 32D05; Secondary 32A07, 32D10
MathSciNet review: 906821
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Abstract: The paper presents a large class of domains $ G$ of holomorphy in $ {{\mathbf{C}}^n}$ such that, for any $ N > 0$, there exists a nonextendable holomorphic function $ f$ on $ G$ with $ \vert f\vert\delta _G^N$ bounded where $ {\delta _G}(z): = \min ({(1 + \vert z{\vert^2})^{ - 1 / 2}},\,\operatorname{dist} (z,\,\partial G))$. Any fat Reinhardt domain of holomorphy belongs to this class.

On the other hand we characterize those Reinhardt domains of holomorphy which are existence domains of bounded holomorphic functions.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0906821-9
Article copyright: © Copyright 1987 American Mathematical Society