@article{Zabolotskyi_Zabolotskyi_Tarasyuk_Hal_2024, title={Regular behavior of subharmonic in space functions of the zero kind}, volume={16}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/6125}, DOI={10.15330/cmp.16.1.84-92}, abstractNote={<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 $r\to+\infty$, $0&lt;\rho&lt;1$. 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>}, number={1}, journal={Carpathian Mathematical Publications}, author={Zabolotskyi, M.V. and Zabolotskyi, T.M. and Tarasyuk, S.I. and Hal, Yu.M.}, year={2024}, month={May}, pages={84–92} }