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

DOI10.21136/MB.2017.0110-16zbMath1474.32001OpenAlexW2775234942MaRDI QIDQ4647007

N. V. Petrechko, O. B. Skaskiv, Andriy Bandura

Publication date: 3 January 2019

Published in: Mathematica Bohemica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/mb.2017.0110-16

zbMATH Keywords

analytic functionpartial derivativebidiscmaximum modulusCauchy's integral formulabounded {\textbf{L}}-index in joint variables

Mathematics Subject Classification ID

Special families of functions of several complex variables (32A17) Other generalizations of function theory of one complex variable (32A30) Holomorphic functions of several complex variables (32A10) Quasi-analytic and other classes of functions of one complex variable (30D60)

Related Items (17)

Slice holomorphic functions in the unit ball: boundedness of \(L\)-index in a direction and related properties ⋮ Analytic in a unit polydisc functions of bounded \(L\)-index in direction ⋮ Unnamed Item ⋮ Entire multivariate vector-valued functions of bounded \(\mathbf{L} \)-index: analog of Fricke's theorem ⋮ Entire functions of bounded index in frame ⋮ Note on composition of entire functions and bounded \(L\)-index in direction ⋮ Entire curves having bounded \(l\)-index in \(\ell_{\infty}\) ⋮ Some criteria of boundedness of the \(L\)-index in direction for slice holomorphic functions of several complex variables ⋮ Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables ⋮ Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables ⋮ Slice holomorphic functions in several variables with bounded \(L\)-index in direction ⋮ Analogs of Hayman's theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded L-index in joint variables ⋮ Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded \(\mathbf{L}\)-index in joint variables ⋮ Boundedness of L-index in joint variables for composition of analytic functions in the unit ball ⋮ Some weaker sufficient conditions of $L$-index boundedness in direction for functions analytic in the unit ball ⋮ Functions analytic in the unit ball having bounded \(L\)-index in a direction ⋮ Local properties of the entire functions of bounded index in a frame

Cites Work

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• The space of entire in \({\mathbb C}^{n}\) functions of bounded \(L\)-index
• Analytic functions of bounded \(l\)-index
• Analytic in a polydisc functions of bounded \(L\)-index in joint variables
• Sufficient conditions of boundedness of \(L\)-index in joint variables
• Entire functions of several variables of bounded index
• Differential inequalities and local valency

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