Analytic in an unit ball functions of bounded L-index in joint variables

Abstract

A concept of boundedness of the L-index in joint variables (see in Bandura A. I., Bordulyak M. T., Skaskiv O. B. Sufficient conditions of boundedness of L-index in joint variables, Mat. Stud. 45 (2016), 12–26) is generalized for analytic in a ball function. It is proved criteria of boundedness of the L-index in joint variables which describe local behavior of partial derivatives on a skeleton of a polydisc.