2017
Том 69
№ 7

All Issues

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

Sevost'yanov E. A.


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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 6, pp 938-947.

Citation Example: Sevost'yanov E. A. Analog of the Montel Theorem for Mappings of the Sobolev Class with Finite Distortion // Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 829-837.