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

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.