Continuation of separately harmonic functions along a fixed direction

In this talk we prove that if $u(x,y)$ is a separately harmonic function in the domain $D\times V\subset {{\mathbb{R}}^{n}}\times {{\mathbb{R }}^{2}}$ and for each fixed ${{x}_{0}}\in E\subset D$, where $E$ is not $h$-pluripolar, the function $u({{x} _{0}},y)$ has harmonic continuation to the entire plane ${{\mathbb{R}}^{2}}$, then $u(x,y)$ has harmonic continuation to the domain $D\times {{\mathbb{R}}^{2}}$.