Dirichlet problem for pluriholomorphic functions of two complex variables

In this paper the Dirichlet problem for pluriholomorphic functions of two complex variables is investigated. The key point is the relation between pluriholomorphic functions and pluriharmonic functions. The link is constituted by the Fueter-regular functions of one quaternionic variable. Previous results about the boundary values of pluriharmonic functions and new results on L² traces of regular functions are applied to obtain a characterization of the traces of pluriholomorphic functions.