Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

Logarithmic derivative estimates of meromorphic functions in the half-plane

  • I.E. Chyzhykov Ivan Franko National University of Lviv, Ukraine, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
  • A.Z. Mokhon'ko National University Lviv Polytechnic
Keywords: half-plane, meromorphic function, logarithmic derivative

Abstract

We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.
Examples show that size of exceptional sets are best possible in some sense.

Author Biography

I.E. Chyzhykov, Ivan Franko National University of Lviv, Ukraine, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

Department of Mechanics and Mathematics, Professor

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Published
2020-12-25
How to Cite
1.
Chyzhykov I, Mokhon’ko A. Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane: Logarithmic derivative estimates of meromorphic functions in the half-plane. Mat. Stud. [Internet]. 2020Dec.25 [cited 2021Jan.24];54(2):172-87. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/151
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