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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 6, Pages 21–34 (Mi izv664)  

This article is cited in 1 scientific paper (total in 1 paper)

$C^m$-extension of subholomorphic functions from plane Jordan domains

O. A. Zorina


Abstract: 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 $m\in(0,2]$.

DOI: https://doi.org/10.4213/im664

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English version:
Izvestiya: Mathematics, 2005, 69:6, 1099–1111

Bibliographic databases:

UDC: 517.5
MSC: 31A05, 41A30
Received: 23.05.2005

Citation: O. A. Zorina, “$C^m$-extension of subholomorphic functions from plane Jordan domains”, Izv. RAN. Ser. Mat., 69:6 (2005), 21–34; Izv. Math., 69:6 (2005), 1099–1111

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Boivin, P. M. Gauthier, P. V. Paramonov, “Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfaces”, Sb. Math., 206:1 (2015), 3–23  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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