Supremum and infimum of subharmonic functions of order between 1 and 2
Supremum and infimum of subharmonic functions of order between 1 and 2
Abstract For functions u , subharmonic in the plane, let and let N ( r,u ) be the integrated counting function. Suppose that $\mathcal{N}\colon[0,\infty)\rightarrow\mathbb{R}$ is a non-negative non-decreasing convex function of log r for which $\mathcal{N}(r)=0$ for all small r and $\limsup_{r\to\infty}\log\mathcal{N}(r)/\4\log r=\rho$ , where 1 < ρ < 2, …