TY - JOUR
AU - Zabolotskyi, M.V.
AU - Zabolotskyi, T.M.
AU - Tarasyuk, S.I.
AU - Hal, Yu.M.
PY - 2024/05/12
Y2 - 2024/11/13
TI - Regular behavior of subharmonic in space functions of the zero kind
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 16
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.16.1.84-92
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/6125
SP - 84-92
AB - <p>Let $u$ be a subharmonic in $\mathbb{R}^m$, $m\geq 3$, function of the zero kind with Riesz measure $\mu$ on negative axis $Ox_1$, $n(r,u)=\mu\left(\{x\in\mathbb{R}^m \colon |x|\leq r\}\right)$, \[N(r,u)=(m-2)\int_1^r n(t,u)/t^{m-1}dt,\] $\rho(r)$ is a proximate order, $\rho(r)\to\rho$ as $r\to+\infty$, $0<\rho<1$. We found the asymptotic of $u(x)$ as $|x|\to+\infty$ by the condition $N(r,u)=\left(1+o(1)\right)r^{\rho(r)}$, $r\to+\infty$. We also investigated the inverse relationship between a regular growth of $u$ and a behavior of $N(r,u)$ as $r\to+\infty$.</p>
ER -