Analog of the Montel Theorem for Mappings of the Sobolev Class with Finite Distortion

Abstract

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.