Analytic functions in a bidisc of bounded $\mathbf{L}$-index in joint variables
Complex Variables
2017-05-30 v1
Abstract
A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in 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 -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 -index in joint variables are obtained.
Keywords
Cite
@article{arxiv.1609.04190,
title = {Analytic functions in a bidisc of bounded $\mathbf{L}$-index in joint variables},
author = {A. I. Bandura and N. V. Petrechko and O. B. Skaskiv},
journal= {arXiv preprint arXiv:1609.04190},
year = {2017}
}
Comments
23 pages