Controlled diffeomorphic extension of homeomorphisms

Let $\mathrm{\Omega }$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$beahomeomorphism\mathrm{.}Weshowthat$\varphi$ has finite dyadic energy if and only if $\phi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy.