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): B^2→R^2_+ is a positive continuous vector-function, B^2={zC^2: |z|=|z_1|^2+|z_2|^21}. 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.