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 $\{z:|z|<1\},\ h\in H$ 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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Vasyl Stefanyk Precarpathian National University
2013-01-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/51 |
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doaj-7679ec3872664ea6afca51788b56bc522020-11-25T00:46:44ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-01-012110911810.15330/cmp.2.1.109-11856Direct analogues of Wiman's inequality for analytic functions in the unit discO. B. Skaskiv0A. O. Kuryliak1Ivan Franko National University, 1 Universytetska str., 79000, Lviv, UkraineIvan Franko National University of LvivLet $f(z)=\sum_{n=0}^{\infty} a_n z^n$ be an analytic function on $\{z:|z|<1\},\ h\in H$ and $\Omega_f(r)= \sum_{n=0}^{\infty} |a_n| r^n$. If<br />$$<br />\beta_{fh}=\liminf\limits_{r\to1}\frac{\ln\ln\Omega_f(r)}{\ln h(r)}=+\infty,<br />$$<br />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 $h-\mbox{meas}\ E<+\infty.$http://journals.pu.if.ua/index.php/cmp/article/view/51 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
O. B. Skaskiv A. O. Kuryliak |
| spellingShingle |
O. B. Skaskiv A. O. Kuryliak Direct analogues of Wiman's inequality for analytic functions in the unit disc Karpatsʹkì Matematičnì Publìkacìï |
| author_facet |
O. B. Skaskiv A. O. Kuryliak |
| author_sort |
O. B. Skaskiv |
| title |
Direct analogues of Wiman's inequality for analytic functions in the unit disc |
| title_short |
Direct analogues of Wiman's inequality for analytic functions in the unit disc |
| title_full |
Direct analogues of Wiman's inequality for analytic functions in the unit disc |
| title_fullStr |
Direct analogues of Wiman's inequality for analytic functions in the unit disc |
| title_full_unstemmed |
Direct analogues of Wiman's inequality for analytic functions in the unit disc |
| title_sort |
direct analogues of wiman's inequality for analytic functions in the unit disc |
| publisher |
Vasyl Stefanyk Precarpathian National University |
| series |
Karpatsʹkì Matematičnì Publìkacìï |
| issn |
2075-9827 2313-0210 |
| publishDate |
2013-01-01 |
| description |
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<br />$$<br />\beta_{fh}=\liminf\limits_{r\to1}\frac{\ln\ln\Omega_f(r)}{\ln h(r)}=+\infty,<br />$$<br />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 $h-\mbox{meas}\ E<+\infty.$ |
| url |
http://journals.pu.if.ua/index.php/cmp/article/view/51 |
| work_keys_str_mv |
AT obskaskiv directanaloguesofwimansinequalityforanalyticfunctionsintheunitdisc AT aokuryliak directanaloguesofwimansinequalityforanalyticfunctionsintheunitdisc |
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1725263428447109120 |