Direct analogues of Wiman's inequality for analytic functions in the unit disc

Keywords: Wiman's inequality, analytic function
Published online: 2010-06-30

Abstract


Let $f(z)=\sum_{n=0}^{\infty} a_n z^n$ be an analytic function on $\{z:|z|<1\},\ h\in H$ and $\Omega_f(r)= \sum_{n=0}^{\infty} |a_n| r^n$. If $$ \beta_{fh}=\varliminf\limits_{r\to1}\frac{\ln\ln\Omega_f(r)}{\ln h(r)}=+\infty, $$ then Wiman's inequality $M_f(r)\leq \mu_f(r) \ln^{1/2+\delta}\mu_f(r)$ is true for all $r\in (r_0, 1)\backslash E(\delta)$, where $h-\mbox{meas}\ E<+\infty.$

How to Cite
(1)
Skaskiv O., Kuryliak A. Direct Analogues of Wiman’s Inequality for Analytic Functions in the Unit Disc. Carpathian Math. Publ. 2010, 2 (1), 109-118.

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