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.
Similar content being viewed by others
REFERENCES
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).
A. A. Kondratyuk and Ya. V. Vasyl'kiv, “Conjugate of subharmonic function,” Mat. Studii, 13, No. 2, 173–180 (2000).
W. Hayman and P. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).
H. Skoda, “Sous-ensembles analytique d'ordre fini ou infini dans ℂn,” Bull. Soc. Math. France, 100, No. 4, 353–408 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vasyl'kiv, Y.V. On the Growth of Infinite-Order Subharmonic Functions in ℂ. Ukrainian Mathematical Journal 54, 1540–1546 (2002). https://doi.org/10.1023/A:1023424120570
Issue Date:
DOI: https://doi.org/10.1023/A:1023424120570