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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - O. A. Zorina
TI  - $C^m$-extension of subholomorphic functions from plane Jordan domains
JO  - Izvestiya. Mathematics 
PY  - 2005
SP  - 1099
EP  - 1111
VL  - 69
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a1/
LA  - en
ID  - IM2_2005_69_6_a1
ER  - 
%0 Journal Article
%A O. A. Zorina
%T $C^m$-extension of subholomorphic functions from plane Jordan domains
%J Izvestiya. Mathematics 
%D 2005
%P 1099-1111
%V 69
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2005_69_6_a1/
%G en
%F IM2_2005_69_6_a1
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/

[1] Zorina O. A., “O nepreryvnom prodolzhenii subgolomorfnykh funktsii”, Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 2004, no. 4, 30–36 | MR | Zbl

[2] Paramonov P. V., “O $C^m$-prodolzhenii reshenii odnorodnykh ellipticheskikh neravenstv”, Tez. dokladov 11-i Saratovskoi zimnei shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya”, Saratov, 2002, 149–150

[3] Paramonov P. V., “O $C^m$-prodolzhenii subgarmonicheskikh funktsii”, Izv. RAN Ser. matem., 69:6 (2005), 139–152 | MR | Zbl

[4] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR

[5] Verdera Dzh., Melnikov M. S., Paramonov P. V., “$C^1$-approksimatsiya i prodolzhenie subgarmonicheskikh funktsii”, Matem. sb., 192:4 (2001), 37–58 | MR | Zbl

[6] O'Farrell A. G., “Rational approximations in Lipschitz norms, II”, Proc. Royal Irish Acad., 79A (1979), 104–114

[7] Verdera J., “$C^m$-approximations by solutions of elliptic equations and Calderon-Zygmund operators”, Duke Math J., 55:1 (1987), 157–187 | DOI | MR | Zbl

[8] Paramonov P. V., “O garmonicheskikh approksimatsiyakh v $C^1$-norme”, Matem. sb., 181:10 (1990), 1341–1365 | MR

[9] Vekua I. N., Obobschennye analiticheskie funktsii, Fizmatgiz, M., 1959 | MR

[10] Lib E., Loss M., Analiz, Nauch. kniga, Novosibirsk, 1998

[11] Verdera J., “On $C^m$ rational approximations”, Proc. Amer. Math. Soc., 97 (1986), 621–625 | DOI | MR | Zbl

[12] Melnikov M. S., Paramonov P. V., “$C^1$-prodolzhenie subgarmonicheskikh funktsii s zamknutykh zhordanovykh oblastei v $\mathbb R^2$”, Izv. RAN. Ser. matem., 68:6 (2004), 105–118 | MR

[13] Vitushkin A. G., “Analiticheskaya emkost mnozhestv v zadachakh teorii priblizhenii”, UMN, 22:6 (1967), 141–199 | MR