Analytic functions in the unit ball of bounded value L-distribution in a direction
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 1
Abstract
We present a generalization of concept of bounded value L-distribution in direction b∈Cn∖{0} for analytic functions in the unit ball Bn⊂Cn, where L:Bn→R+ is a continuous function. It is established a connection between the class of analytic functions in the unit ball of bounded L-index in the direction b and the class of analytic functions in the unit ball of bounded value L-distribution in the same direction. The main result of the paper is the following: An analytic function F:Bn→C is a function of bounded value L-distribution in a direction b∈Cn∖{0} if and only if its directional derivative ∂F∂b has bounded L-index in the same direction b.
Authors and Affiliations
Andriy Bandura
Keywords
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- EP ID EP355318
- DOI 10.15330/ms.49.1.75-79
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