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Admissible boundary values of bounded holomorphic functions in wedges


Author: Franc Forstnerič
Journal: Trans. Amer. Math. Soc. 332 (1992), 583-593
MSC: Primary 32E35
DOI: https://doi.org/10.1090/S0002-9947-1992-1087055-9
MathSciNet review: 1087055
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Abstract: If $ M \subset {\mathbb{C}^N}$ is a generic Cauchy-Riemann manifold and $ \mathcal{W} \subset {\mathbb{C}^N}$ is a wedge domain with edge $ M$, then every bounded holomorphic function on $ \mathcal{W}$ has an admissible limit at almost every point of $ M$. Moreover, if a holomorphic function $ f$ on $ \mathcal{W}$ has a distribution boundary value $ (\operatorname{bv}\;f)$ on $ M$ that is a bounded measurable function, then $ f$ is bounded on every finer wedge near $ M$ , and its admissible limit equals $ (\operatorname{bv}\;f)(p)$ at almost every point $ p \in M$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1087055-9
Article copyright: © Copyright 1992 American Mathematical Society

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