Analog of Montel theorem for mappings of Sobolev class with finite distortion

Abstract

The present paper is devoted to the study of classes of mappings with non-bounded characteristic of quasiconformality. It is obtained a result on normal families of the open discrete mappings $f:D\rightarrow {\Bbb C}\setminus\{a, b\}$ of the class $W_{loc}^{1, 1}$ having a finite distortion and omitting two fixed values $a\ne b$ in ${\Bbb C},$ maximal dilatations of which has a majorant of the class of finite mean oscillation at every point. In particular, the result mentioned above holds for the so-called $Q$-mappings and is an analog of known Montel theorem for analytic functions.