Geodesic
Metric spaces of bounded analytical functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 102-110.

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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. 
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     author = {Sh. A. Makhmutov and M. S. Makhmutova},
     title = {Metric spaces of bounded analytical functions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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Sh. A. Makhmutov; M. S. Makhmutova. Metric spaces of bounded analytical functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 102-110. http://geodesic.mathdoc.fr/item/INTO_2017_142_a8/