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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 2, Pages 216–247 (Mi msb2680)  

This article is cited in 6 scientific papers (total in 7 papers)

An estimate for the subharmonic difference of subharmonic functions. I

I. F. Krasichkov-Ternovskii


Abstract: Let $u$, $v$ and $w=u-v$ be subharmonic functions in the half-plane $\Pi:\operatorname{Re}\omega>v$ and suppose that $u(\omega)$ and $v(\omega)$ are majorized by a positive function of the form $M(\omega)=\rho T(\rho,\tau)$, where $\rho=|\omega|$ and $\tau=1-\frac2\pi|\arg\omega|$.
An inequality for the subharmonic difference $w=u-v$ is obtained in terms of the function $T(t,\tau)$, $0<t<\infty$, $0<\tau<1$, which then gives an estimate for the difference from above. This inequality is carried over by conformal mappings to a class of regions with cusps (horn regions).
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 31:2, 191–218

Bibliographic databases:

UDC: 517.53
MSC: Primary 31A05, 30A04; Secondary 30A42
Received: 09.02.1976

Citation: I. F. Krasichkov-Ternovskii, “An estimate for the subharmonic difference of subharmonic functions. I”, Mat. Sb. (N.S.), 102(144):2 (1977), 216–247; Math. USSR-Sb., 31:2 (1977), 191–218

Citation in format AMSBIB
\Bibitem{Kra77}
\by I.~F.~Krasichkov-Ternovskii
\paper An estimate for the subharmonic difference of subharmonic functions.~I
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 216--247
\mathnet{http://mi.mathnet.ru/msb2680}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=507987}
\zmath{https://zbmath.org/?q=an:0346.31001|0385.31001}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 191--218
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002298}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977FY72200005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. F. Krasichkov-Ternovskii, “Estimates for the subharmonic difference of subharmonic functions. II”, Math. USSR-Sb., 32:1 (1977), 59–97  mathnet  crossref  mathscinet  zmath  isi
    2. S. A. Apresyan, “Localization of ideals and asymptotic uniqueness theorems for functions with restrictions on growth”, Math. USSR-Sb., 34:5 (1978), 561–592  mathnet  crossref  mathscinet  zmath
    3. Krasichkovternovskii I., “Local Description of Closed Submodules and the Problem of Over-Saturation”, 1043, 1984, 367–371  isi
    4. Borichev A., “Convolution Equations and the Structure of 1-Invariant and 2-Invariant Subspaces in a Scale of Spaces of Rough Growth”, 304, no. 4, 1989, 788–792  mathscinet  zmath  isi
    5. R. S. Yulmukhametov, “Spectral synthesis in the kernel of a convolution operator in weighted spaces”, St. Petersburg Math. J., 21:2 (2010), 353–363  mathnet  crossref  mathscinet  zmath  isi
    6. Zhang Yanhui, Deng Guantie, Kou K.I., “On the Lower Bound for a Class of Harmonic Functions in the Half Space”, Acta Math. Sci., 32:4 (2012), 1487–1494  mathscinet  zmath  isi
    7. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192  mathnet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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