On a boundary analog of the Forelli theorem

A boundary analog of the Forelli theorem for real-analytic functions is established, i.e., it is demonstrated that each real-analytic function $f$ defined on the boundary of a bounded strictly convex domain $D$ in the multidimensional complex space with the one-dimensional holomorphic extension property along families of complex lines passing through a boundary point and intersecting $D$ admits a holomorphic extension to $D$ as a function of many complex variables.