Metric Spaces of Bounded Analytical Functions

S. A. Makhmutov; M. S. Makhmutova

doi:10.1007/s10958-019-04460-1

Metric Spaces of Bounded Analytical Functions

S. A. Makhmutov^*, M. S. Makhmutova

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider classes of analytical functions that map the unit disk into itself. Functions of these classes can be described in terms of hyperbolic derivative and hyperbolic metric. Under an appropriate choice of the corresponding metrics, these classes are metric spaces. Functions of the hyperbolic classes considered generate composition operators from the Bloch space into classical spaces of analytical functions in the unit disk.

Original language	English
Pages (from-to)	750-759
Number of pages	10
Journal	Journal of Mathematical Sciences
Volume	241
Issue number	6
DOIs	https://doi.org/10.1007/s10958-019-04460-1
Publication status	Published - Sept 28 2019

Keywords

30H05
47B33
bounded analytical function
composition operator
hyperbolic derivative
hyperbolic metric

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-019-04460-1

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abstract = "In this paper, we consider classes of analytical functions that map the unit disk into itself. Functions of these classes can be described in terms of hyperbolic derivative and hyperbolic metric. Under an appropriate choice of the corresponding metrics, these classes are metric spaces. Functions of the hyperbolic classes considered generate composition operators from the Bloch space into classical spaces of analytical functions in the unit disk.",

keywords = "30H05, 47B33, bounded analytical function, composition operator, hyperbolic derivative, hyperbolic metric",

author = "Makhmutov, {S. A.} and Makhmutova, {M. S.}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

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AB - In this paper, we consider classes of analytical functions that map the unit disk into itself. Functions of these classes can be described in terms of hyperbolic derivative and hyperbolic metric. Under an appropriate choice of the corresponding metrics, these classes are metric spaces. Functions of the hyperbolic classes considered generate composition operators from the Bloch space into classical spaces of analytical functions in the unit disk.

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KW - composition operator

KW - hyperbolic derivative

KW - hyperbolic metric

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Metric Spaces of Bounded Analytical Functions

Abstract

Keywords

ASJC Scopus subject areas

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