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arXiv · 1609.04190

Analytic functions in a bidisc of bounded $\mathbf{L}$-index in joint variables

A. I. Bandura·N. V. Petrechko·O. B. Skaskiv
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Abstract

A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud., 4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc function. We proved criteria of boundedness of $\mathbf{L}$-index in joint variables which describe local behaviour of partial derivative and give an estimate of maximum modulus on a skeleton of polydisc. Some improvements of known sufficient conditions of boundednees of $\mathbf{L}$-index in joint variables are obtained.

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A. I. Bandura, N. V. Petrechko, O. B. Skaskiv. 2016-09-14. Analytic functions in a bidisc of bounded $\mathbf{L}$-index in joint variables. https://doi.org/10.15330/ms.46.1.72-80

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