I am looking for an elliptic regularity theorem in the Sobolev Space $H^s(\mathbb R^3)$ for $s<0$. In fact we have the equation $$A\,u=f,$$ where $A$ is an elliptic operator and $f\in H^s(\mathbb R^3)$ with $s<0$.
Can we deduce that $u\in H^{s+2}(\mathbb R^3)$?
I am also looking for a good reference in Elliptic Regularity please.