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

  • E. A. Sevost'yanov

Abstract

We study the classes of mappings with unbounded characteristic of quasiconformality and obtain a result on the normal families of open discrete mappings $f : D → ℂ \backslash \{a, b\}$ from the class $W\{\text{loc}^{1,1}$ 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.
Published
25.06.2015
How to Cite
Sevost’yanovE. A. “Analog of the Montel Theorem for Mappings of the Sobolev Class With Finite Distortion”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 6, June 2015, pp. 829-37, http://umj.imath.kiev.ua/index.php/umj/article/view/2025.
Section
Research articles