Mathematica Bohemica, Vol. 143, No. 4, pp. 339-354, 2018

Maximum modulus in a bidisc of analytic functions of bounded ${\mathbf L}$-index and an analogue of Hayman's theorem

Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv

Received December 28, 2016.   First published December 11, 2017.

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).
Keywords:  analytic function; bidisc; bounded ${\mathbf L}$-index in joint variables; maximum modulus; partial derivative; Cauchy's integral formula
Classification MSC:  32A10, 32A17, 32A30, 30D60
DOI:  10.21136/MB.2017.0110-16

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Affiliations:   Andriy Bandura, Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, Karpatska Street 15, Ivano-Frankivsk, Ukraine 76019, e-mail:; Nataliia Petrechko, Oleh Skaskiv, Department of Function Theory and Theory of Probability, Ivan Franko National University of Lviv, Universytetska St. 1, Lviv, 79000L, Ukraine, e-mail:,

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