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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 1, Pages 120–131 (Mi smj1152)  
Stability in the Cauchy and Morera theorems for holomorphic functions and their spatial analogs

A. P. Kopylova, M. V. Korobkova, S. P. Ponomarevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Institute of Mathematics, Pomeranian Pedagogical Academy
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Abstract: Criteria are given for a mapping to have bounded distortion in terms of an integral estimate of the multiplicity function without any a priori assumption on the differential properties of the mapping. The result is most lucid and final in a sense for complex functions $f\colon\Delta\subset\mathbb{C}\to\mathbb{C}$ of one complex variable. Generalizations to multidimensional Beltrami systems are suggested.
Keywords: stability, Cauchy theorem, Morera theorem, holomorphic function, Beltrami system, mapping with bounded distortion.
Received: 12.08.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 1, Pages 99–108
DOI: https://doi.org/10.1023/A:1022068421764
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: A. P. Kopylov, M. V. Korobkov, S. P. Ponomarev, “Stability in the Cauchy and Morera theorems for holomorphic functions and their spatial analogs”, Sibirsk. Mat. Zh., 44:1 (2003), 120–131; Siberian Math. J., 44:1 (2003), 99–108
Citation in format AMSBIB
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\paper Stability in the Cauchy and Morera theorems for holomorphic functions and their spatial analogs
\jour Sibirsk. Mat. Zh.
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\vol 44
\issue 1
\pages 120--131
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\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 1
\pages 99--108
\crossref{https://doi.org/10.1023/A:1022068421764}
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    		Сибирский математический журнал Siberian Mathematical Journal
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