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Ukrainian Mathematical Journal

, Volume 54, Issue 9, pp 1540–1546 | Cite as

On the Growth of Infinite-Order Subharmonic Functions in ℂ

  • Ya. V. Vasyl'kiv
Article
  • 17 Downloads

Abstract

For infinite-order functions u subharmonic in \(\mathbb{C}\) with given restrictions on the Riesz masses of a disk of radius r ∈ (0, +∞), we find majorants for the functions \(B\left( {r,u} \right) = \max \left\{ {\left| {u\left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\) and \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{B} \left( {r,u} \right) = \sup \left\{ {\left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{u} \left( z \right)} \right|:\left| z \right| \leqslant r} \right\}\), where \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{u}\) is a function conjugate to u.

Keywords

Subharmonic Function Function Conjugate Riesz Masse 
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REFERENCES

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    Ya. V. Vasyl'kiv, “On some properties of δ-subharmonic functions of finite λ-type,” in: Proceedings of the 9th Conference of Young Scientists of the Institute of Applied Problems in Mechanics and Mathematics of the Ukrainian Academy of Sciences, (Lviv, May 10–14, 1982,), Part 2, Lviv (1982), pp. 16–22 (Dep. VINITI, No. 324–84).Google Scholar
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    A. A. Kondratyuk and Ya. V. Vasyl'kiv, “Conjugate of subharmonic function,” Mat. Studii, 13, No. 2, 173–180 (2000).Google Scholar
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    W. Hayman and P. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).Google Scholar
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    H. Skoda, “Sous-ensembles analytique d'ordre fini ou infini dans ℂn,” Bull. Soc. Math. France, 100, No. 4, 353–408 (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Ya. V. Vasyl'kiv
    • 1
  1. 1.Lviv National UniversityLviv

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