The Sobolev space of order $s\in\mathbb R$ in $\mathbb R^n$, denoted by $H^s(\mathbb R^n)$, is defined as follows:
$$H^{s}(\mathbb R^n):=\{u\in\mathscr{S}^{'}(\mathbb R^n): \exists f\in L^1_{\textrm{loc}}(\mathbb R^n); (1+|\cdot|^2)f\in L^2(\mathbb R^n)\ \textrm{and}\ \hat{u}=T_f\}.$$
Above $T_f$ is the tempered distribution given by $$\langle T_f, \varphi\rangle:=\int_{\mathbb R^n} f(x)\varphi(x)\ dx,\ \forall \varphi\in C^\infty_0(\mathbb R^n).$$
I'm studying this space in the context of pseudo-differential operators with symbols in the class $S^m_{1, 0}$.
Can anyone recommend me a book or a paper which deals with the compactness of those operators when acting on $H^{s}(\mathbb R^n)$?
Obs: $\mathscr{S}^{'}(\mathbb R^n)$ is the space of continuous linear functionals on the Schwartz Space $\mathscr{S}(\mathbb R^n)$.