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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 142, Complex Analysis, 2017.
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Makhmutov, S.A., Makhmutova, M.S. Metric Spaces of Bounded Analytical Functions. J Math Sci 241, 750–759 (2019). https://doi.org/10.1007/s10958-019-04460-1
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DOI: https://doi.org/10.1007/s10958-019-04460-1