Geodesic
$C^m$-extension of subholomorphic functions from plane Jordan domains
Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1099-1111

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We prove that every function $f$ of class $C^m(\,\overline{D}\,)$ subholomorphic in $D$ can be extended to a subholomorphic function of class $C^m$ in the whole $\mathbb C$ with an estimate for the $C^m$-norm, where $m\in(0,2)$ and $D$ is an arbitrary Jordan $B$-domain in $\mathbb C$. We obtain some corollaries and an analogue of the above assertion for the classes $\operatorname{Lip}^m$ with $m\in(0,2]$. 
@article{IM2_2005_69_6_a1,
     author = {O. A. Zorina},
     title = {$C^m$-extension of subholomorphic functions from plane {Jordan} domains},
     journal = {Izvestiya. Mathematics },
     pages = {1099--1111},
     publisher = {mathdoc},
     volume = {69},
     number = {6},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a1/}
}
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O. A. Zorina. $C^m$-extension of subholomorphic functions from plane Jordan domains. Izvestiya. Mathematics , Tome 69 (2005) no. 6, pp. 1099-1111. http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a1/