Admissible boundary values of bounded holomorphic functions in wedges
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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 $p \in M$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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