Regular behavior of subharmonic in space functions of the zero kind - Zabolotskyi, M.V.; Zabolotskyi, T.M.; Tarasyuk, S.I.; Hal, Yu.M. (Carpathian Mathematical Publications, 2024)
Let u be a subharmonic in R^m, m≥ 3, function of the zero kind with Riesz measure μ on negative axis Ox_1, n(r,u)=μ({xR^m |x|≤ r}), \[N(r,u)=(m-2)_1^r n(t,u)/t^m-1dt,\] ρ(r) is a proximate order, ρ(r)→ρ as r→+∞, 0<ρ<1. We found the asymptotic of u(x) as |x|→+∞ by the condition N(r,u)=(1+o(1))r^ρ(r), r→+∞. We also investigated the inverse relationship between a regular growth of u and a behavior of N(r,u) as r→+∞.