The Pluricomplex Poisson Kernel for Strongly Convex Domains

In the past decades the study of pluri-potential theory and of its applications played a central role in complex analysis in several variables. In particular, since the basic work of Siciak [31] and Bedford and Taylor [7], [8] a great effort was made to understand the complex MongeAmpère operator and the associated generalized Dirichlet problems (for instance, see [15], [20] and references therein). Let D ⊂ C be a bounded convex domain with z0 ∈ D. From the work of Lempert [21], [24] and Demailly [15] it turned out that the following homogeneous Monge-Ampère equation