TY - JOUR
AU - E. A. Sevost'yanov
PY - 2015/06/25
Y2 - 2023/11/29
TI - Analog of the Montel Theorem for Mappings of the Sobolev Class with Finite Distortion
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 6
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2025
AB - 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.
ER -