Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables
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DOI:
https://doi.org/10.15330/cmp.11.2.213-227Keywords:
bounded index, bounded $\mathbf{L}$-index in joint variables, analytic function, unit ball, local behavior, maximum modulus, $\sup$-norm, verctorvalued functionAbstract
In this paper, we consider a class of vector-functions, which are analytic in the unit ball. For this class of functions there is introduced a concept of boundedness of $\mathbf{L}$-index in joint variables, where $\mathbf{L}=(l_1,l_2): \mathbb{B}^2\to\mathbb{R}^2_+$ is a positive continuous vector-function, $\mathbb{B}^2=\{z\in\mathbb{C}^2: |z|=\sqrt{|z_1|^2+|z_2|^2}\le 1\}.$ We present necessary and sufficient conditions of boundedness of $\mathbf{L}$-index in joint variables. They describe the local behavior of the maximum modulus of every component of the vector-function or its partial derivatives.
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Published
2019-12-31
How to Cite
(1)
Baksa, V. Analytic Vector-Functions in the Unit Ball Having Bounded $\mathbf{L}$-Index in Joint Variables: Array. Carpathian Math. Publ. 2019, 11, 213-227.
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Scientific articles