Let $U \subseteq \mathbb{R}^n$ be open, and let $R \in \Psi^{-\infty}(U)$ be a properly supported smoothing pseudodifferential operator. Then for every $s,t \in \mathbb{R}$, the operator $R$ extends continuously as a map
Equivalently, for every $\chi \in C_c^\infty(U)$ there exist $\psi \in C_c^\infty(U)$ and a constant $C_{\chi,\psi,s,t} > 0$ such that $\psi = 1$ on a neighbourhood of the set of points in $U$ on which $R$ can depend when tested on $\operatorname{supp}\chi$, and