### A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Given a domain $\Omega $ of class ${C}^{k,1}$, $k\in \mathbb{N}$, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial -\partial {x}_{n})\alpha ({x}^{\text{'}},0)=-N\left({x}^{\text{'}}\right)$ and that still is of class ${C}^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class ${C}^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.