I need a reference for the following fact. Let $\Omega \subset \mathbb R^n$ be an open domain with $C^{1,1}$ boundary (maybe, less regularity is needed). Let $H^{1/2}(\Gamma)$ be the trace space of $H^1(\Omega)$. Then, the multiplication with a function $\theta \in C^{0,1}(\Gamma)$ is a bounded, linear operator in $H^{1/2}(\Gamma)$.
I think it can be easily proved by using extensions of the functions from $\Gamma$ to $\Omega$, but I think, there should be a nice reference somewhere.