Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables

  • V.P. Baksa Ivan Franko National University, 1 Universytetska str., 79000, Lviv, Ukraine
Keywords: bounded index, bounded $\mathbf{L}$-index in joint variables, analytic function, unit ball, local behavior, maximum modulus, $\sup$-norm, verctorvalued function
Published online: 2019-12-31


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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How to Cite
Baksa V. Analytic Vector-Functions in the Unit Ball Having Bounded $\mathbf{L}$-Index in Joint Variables. Carpathian Math. Publ. 2019, 11 (2), 213-227.