On the Growth of Infinite-Order Subharmonic Functions in ℂ

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.