On traces of Sobolev functions on the boundary of extension domains

Assume that $\Omega\subset\mathbb{R}^N$ is a bounded $W^{1,p}$-extension domain and that $\mu$ is an upper $d$-Ahlfors measure on $\partial\Omega$ with $p\in(1,N)$ and $d\in(N-p,N)$. Then there exist continuous trace operators from $W^{1,p}(\Omega)$ into $L^q(\partial\Omega,d\mu)$ and into $B^p_\beta(\partial\Omega,d\mu)$ for every $q\in[1,dp/(N-p)]$ and every $\beta\in (0,1-(N-d)/p]$.