We study the classes of mappings with unbounded characteristic of quasiconformality and obtain a result on the normal families of open discrete mappings f : D→ ℂ \ {a, b} from the class W loc 1,1 with finite distortion that do not take at least two fixed values a 6≠b in ℂ whose maximal dilatation has a majorant of finite mean oscillation at every point. This result is an analog of the well-known Montel theorem for analytic functions and is true, in particular, for the so-called Q-mappings.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 829–837, June, 2015.
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Sevost’yanov, E.A. Analog of the Montel Theorem for Mappings of the Sobolev Class with Finite Distortion. Ukr Math J 67, 938–947 (2015). https://doi.org/10.1007/s11253-015-1124-y
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DOI: https://doi.org/10.1007/s11253-015-1124-y