Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables
Copyright policy )Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables
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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Holomorphic functions of several complex variables, bounded index, bounded $\mathbf{L}$-index in joint variables, analytic function, unit ball, local behavior, maximum modulus, $\sup$-norm, verctorvalued function, analytic function, Special families of functions of several complex variables, bounded \(\mathbf{L} \)-index, $\sup$-norm, local behavior, обмежений індекс, обмежений $\mathbf{L}$-індекс за сукупністю змінних, аналітична функція, одинична куля, локальне поводження, максимум модуля, $\sup$-норма, векторнозначна функція, QA1-939, bounded $\mathbf{l}$-index in joint variables, verctorvalued function, analytic vector functions in the ball, unit ball, maximum modulus, Mathematics, bounded index
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