A theorem on holomorphic extension of CR-functions (Q1078729)

The author deals with the holomorphic extendability of CR-functions. The following theorem is proved: Let D be a bounded domain in \({\mathbb{C}}^ n\), \(n\geq 2\) and \(K\subset \partial D\) be a compact subset such that \(\partial D\setminus K\) is a real \(C^ 1\) hypersurface of \({\mathbb{C}}^ n\setminus K\). Assume K is \({\mathcal O}(\bar D)\)-convex then every continuous CR-function f on \(\partial D\setminus K\) extends holomorphically on D.