Let $n \in \mathbb{N}$, let $U \subseteq \mathbb{R}^n$ be open, let $r>0$, and let $A \in \Psi^{-r}(U)$ be a properly supported pseudodifferential operator with Schwartz kernel $K_A \in \mathcal{D}'(U \times U)$. Define the support relation of $A$ by
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\begin{align*}
\operatorname{Rel}(A) := \operatorname{supp} K_A \subset U \times U.
\end{align*}
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Then for every $s \in \mathbb{R}$ and every $\chi,\psi \in C_c^\infty(U)$, the localized operator