On traces of Sobolev functions on the boundary of extension domains

Abstract:

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 $\beta \in (0,1-(N-d)/p]$.