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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 1, Pages 221–231
DOI: https://doi.org/10.1070/IM1990v035n01ABEH000697
(Mi im1279)
 

This article is cited in 3 scientific papers (total in 3 papers)

Generalization of a theorem of Men'shov on monogenic functions

D. S. Telyakovskii
References:
Abstract: It is shown that in Men'shov's theorem on the holomorphicity of continuous functions monogenic at each point of a domain with respect to two intervals intersecting at this point the condition of continuity of $f(z)$ may be replaced by the condition of summability of $(\log^+|f(z)|)^p$ for all positive $p<2$. As a collateral result a theorem of Phragmén–Lindelöf type is proved in which a certain summability condition is imposed in place of a condition on the growth of the function.
Bibliography: 17 titles.
Received: 16.10.1987
Bibliographic databases:
UDC: 517.5
MSC: 30A05
Language: English
Original paper language: Russian
Citation: D. S. Telyakovskii, “Generalization of a theorem of Men'shov on monogenic functions”, Math. USSR-Izv., 35:1 (1990), 221–231
Citation in format AMSBIB
\Bibitem{Tel89}
\by D.~S.~Telyakovskii
\paper Generalization of a~theorem of Men'shov on monogenic functions
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 221--231
\mathnet{http://mi.mathnet.ru//eng/im1279}
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000697}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1018753}
\zmath{https://zbmath.org/?q=an:0695.30002|0689.30003}
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  • https://doi.org/10.1070/IM1990v035n01ABEH000697
  • https://www.mathnet.ru/eng/im/v53/i4/p886
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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