Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables
- Authors: Bandura A.I.1, Skaskiv O.B.2
-
Affiliations:
- Ivano-Frankivsk National Technical University of Oil and Gas
- Ivan Franko National University of Lviv
- Issue: Vol 239, No 1 (2019)
- Pages: 17-29
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242618
- DOI: https://doi.org/10.1007/s10958-019-04284-z
- ID: 242618
Cite item
Abstract
We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where \( L:{\mathbb{C}}^n\to {\mathbb{R}}_{+}^n \) is a continuous positive vector-function. They give an stimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives outside some exceptional set and the distribution of zeros. The deduced results are also new for analytic functions in the unit disc of bounded index and l-index. They generalize known results by G. H. Fricke, M. M. Sheremeta, A. D. Kuzyk, and V. O. Kushnir.
About the authors
Andriy I. Bandura
Ivano-Frankivsk National Technical University of Oil and Gas
Author for correspondence.
Email: andriykopanytsia@gmail.com
Ukraine, Ivano-Frankivsk
Oleh B. Skaskiv
Ivan Franko National University of Lviv
Email: andriykopanytsia@gmail.com
Ukraine, Lviv