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

Abstract

In 1955, Lehto showed that, for every measurable function $\psi$ on the unit circle $\mathbb{T},$ there is function $f$ holomorphic in the unit disc $\mathbb{D},$ having $\psi$ as radial limit a.e. on $\mathbb{T}.$ 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 $p.$