Beltrami equation with coefficient in Sobolev and Besov spaces

Our goal in this work is to present some function spaces on the complex plane $\text{C}$, $X(\text{C})$, for which the quasiregular solutions of the Beltrami equation, $\bar{\mathrm{\partial }}f(z)=\mu (z)\mathrm{\partial }f(z)$, have first derivatives locally in $X(\text{C})$, provided that the Beltrami coefficient $\mu$ belongs to $X(\text{C})$.