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

2021/03/18 by Gauthier, Paul M., Shirazi, Mohammad
#30E25 (Primary) 30E10 (Secondary) #32A40 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.10032

Abstract

In 1955, Lehto showed that, for every measurable function ψ on the unit circle \mathbb T, there is function f holomorphic in the unit disc \mathbb D, having ψ 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.

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