Geodesic
Asymptotic first boundary value problem for holomorphic functions of several complex variables
Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 361-380

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DOI

In 1955, Lehto showed that, for every measurable function $\psi $ on the unit circle ${\mathbb T}$, there is a 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.
DOI : 10.4153/S0008439521000321
Mots-clés : Boundary values, holomorphic functions, complex approximation 
Gauthier, Paul M.; Shirazi, Mohammad. Asymptotic first boundary value problem for holomorphic functions of several complex variables. Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 361-380. doi: 10.4153/S0008439521000321
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     title = {Asymptotic first boundary value problem for holomorphic functions of several complex variables},
     journal = {Canadian mathematical bulletin},
     pages = {361--380},
     year = {2022},
     volume = {65},
     number = {2},
     doi = {10.4153/S0008439521000321},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000321/}
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