Continuous pluriharmonic boundary values

The Dirichlet problem for $m$-subharmonic functions on compact sets

“…Furthermore, for n ≥ 3 the compact set X is a n-Poisson set, since for every f ∈ C(∂D × • • • × ∂D) we can always find a pluriharmonic function u defined on D n such that u = f on ∂D × • • • × ∂D (see e.g. [2,3]).…”