What are the best results on (Sobolev space) trace theorems for $C^{k,1}$ domains?

For $k=0$, e.g., when the domain is Lipschitz, it is known that the trace map is bounded (and has a continuous right inverse) from $H^{s}(\Omega)$ to $H^{s-1/2}(\partial\Omega)$ for $s\in(\frac12,\frac32)$. Moreover the endpoint case $s=\frac32$ is claimed but a proof seems to have not appeared. A part of the question is whether or not the claimed proof appeared. The other part is if there is a proof of the obvious extension of this result to $C^{k,1}$ domains. If so, what is the situation of the corresponding endpoint (i.e., $s=k+\frac32$) result?