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

 

On boundary values of holomorphic functions on balls


Author: Josip Globevnik
Journal: Proc. Amer. Math. Soc. 85 (1982), 61-64
MSC: Primary 32A40
MathSciNet review: 647898
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Abstract: It is a result of Agranovski and Valski for which Nagel and Rudin, and Stout have given alternate proofs, that if $ B$ is the open unit ball in $ {{\mathbf{C}}^n}$ and if $ f \in C(\partial B)$ has the property that for every complex line $ \Lambda \subset {{\mathbf{C}}^n}$, $ f\left\vert {(\Lambda \cap \partial B)} \right.$ has a continuous extension to $ \Lambda \cap \bar B$ which is holomorphic in $ \Lambda \cap B$, then $ f$ has a continuous extension to $ \bar B$ which is holomorphic in $ B$. In the paper we give an easier, more geometric proof of this result and then prove the local version of this result.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0647898-9
PII: S 0002-9939(1982)0647898-9
Article copyright: © Copyright 1982 American Mathematical Society