Analytic vector-functions in the unit ball having bounded $L$-index in joint variables - Baksa, V.P. (Carpathian Mathematical Publications, 2019)
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 $L$-index in joint variables, where $L=(l_1,l_2): \mathbb{B}^2→\mathbb{R}^2_+$ 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 $L$-index in joint variables. They describe the local behavior of the maximum modulus of every component of the vector-function or its partial derivatives.