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${z:|z|<1}, hin H$ and$Omega_f(r)= sum_{n=0}^{infty} |a_n| r^n$. If$$eta_{fh}=varliminflimits_{ro1}frac{lnlnOmega_f(r)}{ln h(r)}=+infty,$$then Wiman's inequality$M_f(r)leq mu_f(r) ln^{1/2+delta}mu_f(r)$is true for all $rin (r_0,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2010-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/51/43 |
| _version_ | 1818303599524970496 |
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| author | Skaskiv O.B. Kuryliak A.O. |
| author_facet | Skaskiv O.B. Kuryliak A.O. |
| author_sort | Skaskiv O.B. |
| collection | DOAJ |
| description | Let $f(z)=sum_{n=0}^{infty} a_n z^n$ be an analytic function on${z:|z|<1}, hin H$ and$Omega_f(r)= sum_{n=0}^{infty} |a_n| r^n$. If$$eta_{fh}=varliminflimits_{ro1}frac{lnlnOmega_f(r)}{ln h(r)}=+infty,$$then Wiman's inequality$M_f(r)leq mu_f(r) ln^{1/2+delta}mu_f(r)$is true for all $rin (r_0, 1)ackslash E(delta)$, where $h-mbox{meas} E<+infty.$ |
| first_indexed | 2024-12-13T05:57:22Z |
| format | Article |
| id | doaj.art-b167cde3ec6945efa75cf3d1a893d1fb |
| institution | Directory Open Access Journal |
| issn | 2075-9827 |
| language | English |
| last_indexed | 2024-12-13T05:57:22Z |
| publishDate | 2010-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-b167cde3ec6945efa75cf3d1a893d1fb2022-12-21T23:57:25ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272010-06-0121109118Direct analogues of Wiman's inequality for analytic functions in the unit discSkaskiv O.B.Kuryliak A.O.Let $f(z)=sum_{n=0}^{infty} a_n z^n$ be an analytic function on${z:|z|<1}, hin H$ and$Omega_f(r)= sum_{n=0}^{infty} |a_n| r^n$. If$$eta_{fh}=varliminflimits_{ro1}frac{lnlnOmega_f(r)}{ln h(r)}=+infty,$$then Wiman's inequality$M_f(r)leq mu_f(r) ln^{1/2+delta}mu_f(r)$is true for all $rin (r_0, 1)ackslash E(delta)$, where $h-mbox{meas} E<+infty.$http://journals.pu.if.ua/index.php/cmp/article/view/51/43 |
| spellingShingle | Skaskiv O.B. Kuryliak A.O. Direct analogues of Wiman's inequality for analytic functions in the unit disc Karpatsʹkì Matematičnì Publìkacìï |
| title | 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_short | 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 |
| url | http://journals.pu.if.ua/index.php/cmp/article/view/51/43 |
| work_keys_str_mv | AT skaskivob directanaloguesofwimansinequalityforanalyticfunctionsintheunitdisc AT kuryliakao directanaloguesofwimansinequalityforanalyticfunctionsintheunitdisc |