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