# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333094

Arkiv for Matematik, 45, (1), 105-122, 2005.10
Let X and Y be two complex manifolds, let\$D\$⊂\$X\$and\$G\$⊂\$Y\$be two nonempty open sets, let\$A\$(resp.\$B\$) be an open subset of ∂\$D\$(resp. ∂\$G\$), and let\$W\$be the 2-fold cross ((\$D\$∪\$A\$)×\$B\$)∪(\$A\$×(\$B\$∪\$G\$)). Under a geometric condition on the boundary sets\$A\$and\$B\$, we show that every function locally bounded, separately continuous on\$W\$, continuous on\$A\$×\$B\$, and separately holomorphic on (\$A\$×\$G\$)∪(\$D\$×\$B\$) “extends” to a function continuous on a “domain of holomorphy” \$\widehat{W}\$ and holomorphic on the interior of \$\widehat{W}\$ .
```@inproceedings{peter2005generalization,
title={Generalization of a theorem of Gonchar},
author={Peter Pflug, and Viêt-Anh Nguyên},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203618648109903},
booktitle={Arkiv for Matematik},
volume={45},
number={1},
pages={105-122},
year={2005},
}
```
Peter Pflug, and Viêt-Anh Nguyên. Generalization of a theorem of Gonchar. 2005. Vol. 45. In Arkiv for Matematik. pp.105-122. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203618648109903.