Pluriharmonic extension in proper image domains

Abstract

Abstract. Let Dj be a bounded hyperconvex domain in C n j and set D = D1 × · · · × Ds, j = 1, . . . , s, s ≥ 3. Also let Ωπ be the image of D under the proper holomorphic map π. We characterize those continuous functions f : ∂Ωπ → R that can be extended to a real-valued pluriharmonic function in Ωπ.