Affiliation:
1. Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska Street, 76019 Ivano-Frankivsk, Ukraine
Abstract
In this paper, the following composite analytic functions [Formula: see text] and [Formula: see text] are considered, where [Formula: see text] [Formula: see text] [Formula: see text] We established conditions which provide equivalence of boundedness of the [Formula: see text]-index of the function [Formula: see text] and boundedness of the [Formula: see text]-index in joint variables of the function [Formula: see text] where [Formula: see text] is a continuous function, [Formula: see text] [Formula: see text] For the function [Formula: see text] with additional restrictions, the function [Formula: see text] is constructed such that [Formula: see text] has bounded [Formula: see text]-index in joint variables in the case when the function [Formula: see text] has bounded [Formula: see text]-index in the direction [Formula: see text], where [Formula: see text] is a positive continuous function. Our proofs are based on the application of analog of Hayman’s theorem for these classes of functions.
Publisher
World Scientific Pub Co Pte Lt
Cited by
1 articles.
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