Let $M$ be a closed smooth manifold, and let $H^t(M)$ denote the standard scalar [Sobolev space](/page/Sobolev%20Space) of order $t \in \mathbb{R}$ on $M$. Let $m,s \in \mathbb{R}$, and let $A \in \Psi^m_{\mathrm{cl}}(M)$ be an elliptic classical pseudodifferential operator acting on scalar distributions on $M$. If $u \in \mathcal{D}'(M)$ and $Au \in H^s(M)$, then $u \in H^{s+m}(M)$.