Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 142, Pages 102–110 (Mi into257)  
Metric spaces of bounded analytical functions

Sh. A. Makhmutov, M. S. Makhmutova

Sultan Qaboos University
Full-text PDF (199 kB)
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: bounded analytical function, hyperbolic derivative, hyperbolic metric, composition operator.
Funding agency Grant number
Sultan Qaboos University IG/SCI/DOMS/16/02
This work was supported by the Grant of the Sultan Qaboos University (project No. IG/SCI/DOMS/16/02).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 6, Pages 750–759
DOI: https://doi.org/10.1007/s10958-019-04460-1
Bibliographic databases:
Document Type: Article
UDC: 517.544.4, 517.983
MSC: 30H05, 47B33
Language: Russian
Citation: Sh. A. Makhmutov, M. S. Makhmutova, “Metric spaces of bounded analytical functions”, Complex analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 142, VINITI, M., 2017, 102–110; Journal of Mathematical Sciences, 241:6 (2019), 750–759
Citation in format AMSBIB
\Bibitem{MakMak17}
\by Sh.~A.~Makhmutov, M.~S.~Makhmutova
\paper Metric spaces of bounded analytical functions
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 142
\pages 102--110
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into257}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801353}
\zmath{https://zbmath.org/?q=an:1426.30042}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 6
\pages 750--759
\crossref{https://doi.org/10.1007/s10958-019-04460-1}
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