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

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

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
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
3. Krasichkovternovskii I., “Local Description of Closed Submodules and the Problem of Over-Saturation”, 1043, 1984, 367–371
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
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
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
7. “Igor Fedorovich Krasichkov-Ternovskii (13.02.1935–08.03.2012)”, Ufimsk. matem. zhurn., 4:3 (2012), 187–192
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