Regular behavior of subharmonic in space functions of the zero kind

Let u be a subharmonic in Rᵐ, m≥ 3, function of the zero kind with Riesz measure μ on negative axis Ox₁, n(r,u)=μ(ᵐ |x|≤ r\), \[N(r,u)=(m-2)∫_1^r n(t,u)/tᵐ⁻¹dt,\] 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))rρ(r), r→+∞. We also investigated the inverse relationship between a regular growth of u and a behavior of $N(r,u)$ as r→+∞.