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Analytic in a polydisc functions of bounded $$L$$-index in joint variables. (English) Zbl 1373.30043
Summary: A concept of boundedness of $${\mathbf L}$$-index in joint variables (see M. T. Bordulyak [ibid. 4, 53–58 (1995; Zbl 1023.32500); the first author et al., ibid. Mat. Stud. 45, No. 1, 12–26 (2016; Zbl 1353.30030)]) is generalised for an analytic function in a polydisc. We proved criteria of boundednees of $${\mathbf L}$$-index in joint variables which describe local behaviour of partial derivative. Some improvements of known sufficient conditions of boundednees of $${\mathbf L}$$-index in joint variables are obtained.

##### MSC:
 30D60 Quasi-analytic and other classes of functions of one complex variable 32A10 Holomorphic functions of several complex variables 32A40 Boundary behavior of holomorphic functions of several complex variables
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