I know that we have Rellich-Kondrachov Theorem that says that there is a compact embedding between $H^{1}(\Omega)$ and $H^{0}(\Omega)$, or more generally as Adams states (pag 168 theorem 6.3) we have a compact embedding between $H^{j+k}(\Omega)$ and $H^{j}(\Omega)$ for $j\geq 0$ and $k>0$ integers. So, we are excluding negative exponents, so i would like to know if we can have the same result for every Sobolev Space,i.e, i would like to know if we can have the compact embedding between $H^{m+1}(\Omega)$ and $H^{m}(\Omega)$, $m \in \mathbb{R}$, just knowing Rellich-Kondrachov theorem. I'm particularly interested in knowing if there is a compact embedding for $H^{-1}(\Omega)$ and $H^{0}(\Omega)$.
Thank you in advance, and any reference or help would be useful