We denote by $H^{s}(\Omega)=W^{s,2}(\Omega), s \geqq 0$, the standard Sobolev space of order $s$ based on $L^{2}(\Omega)$, with norm $\|\cdot\|_{s, \Omega}$. Auther writes following.
It is well known that $$ C^{\prime}\|\phi\|_{W^{\frac{1}{2}, 2}(\partial \Omega)} \leqq \inf _{\substack{\left.v \in H^{1}(\Omega) \\ v\right|_{\partial\Omega}=\phi}}\|v\|_{W^{1, 2}(\Omega)} \leqq C\|\phi\|_{W^{\frac{1}{2}, 2}(\partial \Omega)}. $$
Now I do not able to find such result hold for $W^{s,p}(\Omega)$ space. Please give me some reference. I was expecting result like, trace space $ W^{s,p}(\Omega)$ is $W^{s-\frac{1}{p},p}(\Omega)$.
Any help or refernce will be highly appreciated.