Behavior of subharmonic functions of slow growth outside exclusive sets

• Date: 2024
• Main Authors: Zabolotskyy, M., Zabolotskyy, T., Заболоцький, Микола, Заболоцький, Тарас
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8157
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC517.53 Let $v$ be a slowly growing function unbounded on $[0,\,+\infty),$ $u$ be subharmonic (in plane) function of zero order, $\mu$~be its Riesz measure, $n(t,u)=\mu(\{x\colon |x|\le t\}),$ $N(t,u)=\int_{1}^{t}n(\tau,u)/\tau d\tau,$ and $n(r,u)=O(v(r)),$ $r\to+\infty.$ &nbs...