Asymptotic first boundary value problem for holomorphic functions of several complex variables

Abstract

In 1955, Lehto showed that, for every measurable function ψ on the unit circle T, there is function f holomorphic in the unit disc D, having ψ as radial limit a.e. on T. We consider an analogous boundary value problem, where the unit disc is replaced by a Stein domain on a complex manifold and radial approach to a boundary point p is replaced by (asymptotically) total approach to p.