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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 4, Pages 886–896 (Mi izv1279)  

This article is cited in 2 scientific papers (total in 2 papers)

Generalization of a theorem of Men'shov on monogenic functions

D. S. Telyakovskii


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.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:1, 221–231

Bibliographic databases:

UDC: 517.5
MSC: 30A05
Received: 16.10.1987

Citation: D. S. Telyakovskii, “Generalization of a theorem of Men'shov on monogenic functions”, Izv. Akad. Nauk SSSR Ser. Mat., 53:4 (1989), 886–896; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 4
\pages 886--896
\mathnet{http://mi.mathnet.ru/izv1279}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018753}
\zmath{https://zbmath.org/?q=an:0695.30002|0689.30003}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 1
\pages 221--231
\crossref{https://doi.org/10.1070/IM1990v035n01ABEH000697}


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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. E. P. Dolzhenko, “The work of D. E. Men'shov in the theory of analytic functions and the present state of the theory of monogeneity”, Russian Math. Surveys, 47:5 (1992), 71–102  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. D. S. Telyakovskii, “A Generalization of Men'shov's Theorem on Functions Satisfying Condition $K"$”, Math. Notes, 76:4 (2004), 534–545  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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