Admissible boundary values of bounded holomorphic functions in wedges

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 $p \in M$.