TY - JOUR
AU - Chyzhykov, I.E.
AU - Mokhon'ko, A.Z.
PY - 2020/12/25
Y2 - 2021/12/09
TI - Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane: Logarithmic derivative estimates of meromorphic functions in the half-plane
JF - Matematychni Studii
JA - Mat. Stud.
VL - 54
IS - 2
SE - Articles
DO - 10.30970/ms.54.2.172-187
UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/151
SP - 172-187
AB - 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.
ER -