Analytic functions in the unit ball of bounded L-index: asymptotic and local properties
Journal Title: Математичні Студії - Year 2017, Vol 48, Issue 1
Abstract
We have generalized some criteria of boundedness of L-index in joint variables for analytic functions in the unit ball, where L:Bn→Rn+ is a continuous vector-function, Bn is the unit ball in Cn. One of propositions gives an estimate of the coefficients of power series expansions by a dominating homogeneous polynomial for analytic functions in the unit ball. Also we provide growth estimates of these functions. They describe the behavior of maximum modulus of analytic function on a skeleton in a polydisc by behavior of the function L. Most of our results are based on polydisc exhaustion of the unit ball. Nevertheless, we have generalized criteria of boundedness of L-index in joint variables which describe local behavior of partial derivatives on sphere in Cn. The proposition uses a ball exhaustion. An analog of Hayman's theorem is applied to investigation of boundedness of L-index in joint variables for analytic solutions in the unit ball of some linear higher-order systems of PDE's. There were found sufficient conditions providing the boundedness. Growth estimates of analytic solutions in the unit ball are also obtained.
Authors and Affiliations
Andriy Bandura, Oleh Skaskiv
Keywords
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- EP ID EP302715
- DOI 10.15330/ms.48.1.37-73
- Views 60
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