Let $U \subset \mathbb{R}^n$ be open, let $m,s \in \mathbb{R}$, and let $A \in \Psi^m_{1,0}(U)$ be a properly supported pseudodifferential operator. Then $A$ extends uniquely from $C_c^\infty(U)$ to a continuous [linear map](/page/Linear%20Map)
Equivalently, for every cutoff $\chi \in C_c^\infty(U)$ there exist a cutoff $\psi \in C_c^\infty(U)$ and a constant $C>0$ such that, for every $u \in H^s_{\mathrm{loc}}(U)$,