ABSTRACT
In this note, using parametric representation for quasiconformal mappings, we obtain some distortion theorems for JV-set quasiconformal mappings which map the unit disk D onto itself. The results generalize and strengthen some relative results made by Reich-Strebel and Semenov. We also prove an invariant property for JV-set quasiconformal mappings under Möbius transformations of the unit disk D onto itself. As their applications, a better estimate for the complex dilatations of JV-set quasiconformal extensions made by Reich's extension is obtained.
