  Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi :
\mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a
diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study
the relationship between weighted integrability of the derivatives of $h$ and
double integrals of $\varphi$ and of $\varphi^{-1} .$
