  We study when and how the norm of a function $u$ in the homogeneous Sobolev
spaces $\dot{W}^{s, p} (\mathbb{R}^n, \mathbb{R}^m)$, with $p \ge 1$ and either
$s = 1$ or $s > 1/p$, is controlled by the norm of composite function $f \circ
u$ in the same space.
