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

Let $f(z)=\sum_{n=0}^{\infty} a_n z^n$ be an analytic function on $\{z:|z|&lt;1\},\ h\in H$ and $\Omega_f(r)= \sum_{n=0}^{\infty} |a_n| r^n$. If<br />$$<br />\beta_{fh}=\liminf\limits_{r\to1}\frac{\ln\ln\Omega_f(r)}{\ln h(r)}=+\infty,<br />$$<br />then Wiman's inequa...

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Bibliographic Details
Main Authors: O. B. Skaskiv, A. O. Kuryliak
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2013-01-01
Series:Karpatsʹkì Matematičnì Publìkacìï
Online Access:http://journals.pu.if.ua/index.php/cmp/article/view/51