Uniform estimates for local properties of analytic functions in a complete Reinahrdt domain

  • A. I. Bandura Ivano-Frankivsk National Tecnical University of OIl and Gas
  • T.M. Salo Lviv Politechnic National University
Keywords: bounded L-index in joint variables, analytic function, partial derivative, Reinhardt domain


Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus with lesser radii. Such a description is sufficient and necessary  condition of boundedness of $\mathbf{L}$-index in joint variables for functions which are analytic in a complete Reinhardt domain. The vector-valued function $\mathbf{L}$ is a positive and continuous function in the domain and its values at a point is greater than reciprocal of distance from the point to the boundary of the Reinhardt domain multiplied by some constant.

Author Biographies

A. I. Bandura, Ivano-Frankivsk National Tecnical University of OIl and Gas

Ivano-Frankivsk National Technical University of Oil and Gas

Ivano-Frankivsk, Ukraine

T.M. Salo, Lviv Politechnic National University

Lviv Politechnic National University

Lviv, Ukraine


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How to Cite
Bandura, A. I., & Salo, T. (2024). Uniform estimates for local properties of analytic functions in a complete Reinahrdt domain. Matematychni Studii, 61(2), 168-175. https://doi.org/10.30970/ms.61.2.168-175