On the Growth of Infinite-Order Subharmonic Functions in ℂ

  • Ya. V. Kondratyuk

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.
Published
25.09.2002
How to Cite
KondratyukY. V. “On the Growth of Infinite-Order Subharmonic Functions in ℂ”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 9, Sept. 2002, pp. 1276-81, https://umj.imath.kiev.ua/index.php/umj/article/view/4165.
Section
Short communications