On some families of complex lines sufficient for holomorphic extension of functions

Abstract

The present article is based on the result related to the holomorphic extension of functions. Functions with the one-dimensional holomorphic extension property along families of complex lines are discussed. Real analytic functions given on the boundary of a bounded domain $D$ in $\mathbb C^n$, $n>1$ with the one-dimensional holomorphic extension property along families of complex lines are considered. The existence of holomorphic extensions of these functions to $D$ is studied depending on the kind of the domain and location of the families of complex lines.