Asymptotic first boundary value problem for holomorphic functions of several complex variables
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 rep...
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Published in | Canadian mathematical bulletin Vol. 65; no. 2; pp. 361 - 380 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Canada
Canadian Mathematical Society
01.06.2022
Cambridge University Press |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0008-4395 1496-4287 |
DOI: | 10.4153/S0008439521000321 |