English

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 Cn\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 L\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 L\mathbf{L}-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