About distortion theorems for one class quasi-conformal mappings, conformal outside a ring

The author considers the class of quasiconformal homeomorphisms of extended complex plane onto itself, such as $f(\infty)=\infty$, $f'(\infty)=1$, $f(0)=0$. The area theorem was derived in the form of inequality for Grunsky coefficients. This inequality can be used for estimate functionals such as distortion theorems. Sufficient conditions of univalence functions $f(z)$ of this class are given.