Maximum modulus in a bidisc of analytic functions of bounded 𝐋 -index and an analogue of Hayman’s theorem

Andriy Bandura; Nataliia Petrechko; Oleh Skaskiv

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 4, page 339-354
  • ISSN: 0862-7959

Abstract

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We generalize some criteria of boundedness of 𝐋 -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of ( p + 1 ) th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

How to cite

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Bandura, Andriy, Petrechko, Nataliia, and Skaskiv, Oleh. "Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman’s theorem." Mathematica Bohemica 143.4 (2018): 339-354. <http://eudml.org/doc/294506>.

@article{Bandura2018,
abstract = {We generalize some criteria of boundedness of $\mathbf \{L\}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).},
author = {Bandura, Andriy, Petrechko, Nataliia, Skaskiv, Oleh},
journal = {Mathematica Bohemica},
keywords = {analytic function; bidisc; bounded $\{\mathbf \{L\}\}$-index in joint variables; maximum modulus; partial derivative; Cauchy’s integral formula},
language = {eng},
number = {4},
pages = {339-354},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximum modulus in a bidisc of analytic functions of bounded $\{\bf L\}$-index and an analogue of Hayman’s theorem},
url = {http://eudml.org/doc/294506},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Bandura, Andriy
AU - Petrechko, Nataliia
AU - Skaskiv, Oleh
TI - Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman’s theorem
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 339
EP - 354
AB - We generalize some criteria of boundedness of $\mathbf {L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
LA - eng
KW - analytic function; bidisc; bounded ${\mathbf {L}}$-index in joint variables; maximum modulus; partial derivative; Cauchy’s integral formula
UR - http://eudml.org/doc/294506
ER -

References

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  1. Bandura, A., New criteria of boundedness of L-index in joint variables for entire functions, Mat. Visn. Nauk. Tov. Im. Shevchenka 13 (2016), 58-67 Ukrainian. (2016) Zbl06742099
  2. Bandura, A. I., Bordulyak, M. T., Skaskiv, O. B., 10.15330/ms.45.1.12-26, Mat. Stud. 45 (2016), 12-26. (2016) Zbl1353.30030MR3561322DOI10.15330/ms.45.1.12-26
  3. Bandura, A. I., Skaskiv, O. B., Entire Functions of Several Variables of Bounded Index, Chyslo, Lviv (2015). (2015) Zbl1342.32001MR3725018
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  5. Bandura, A. I., Petrechko, N. V., Skaskiv, O. B., 10.15330/ms.46.1.72-80, Mat. Stud. 46 (2016), 72-80. (2016) Zbl1373.30043MR3649050DOI10.15330/ms.46.1.72-80
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