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
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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: andriykopanytsia@gmail.com; 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: petrechko.n@gmail.com, olskask@gmail.com
