Direct analogues of Wiman's inequality for analytic functions in the unit disc - Skaskiv, O.B.; Kuryliak, A.O. (Carpathian Mathematical Publications, 2010)
Let $f(z)=\sum_{n=0}^{∞} a_n z^n$ be an analytic function on $\{z:|z|<1\},\ h\in H$ and $Ω_f(r)= \sum_{n=0}^{∞} |a_n| r^n$. If $$ β_{fh}=\varliminf\limits_{r→1}\frac{\ln\lnΩ_f(r)}{\ln h(r)}=+∞, $$ then Wiman's inequality $M_f(r)≤ μ_f(r) \ln^{1/2+δ}μ_f(r)$ is true for all $r\in (r_0, 1)\backslash E(δ)$, where $h-meas\ E<+∞.$