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arxiv: 1404.4896 · v1 · pith:5EUGZBUJnew · submitted 2014-04-18 · 🧮 math.CV

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

classification 🧮 math.CV
keywords mappingsclassfiniteanalogdistortionmontelresulttheorem
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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.

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