# The inclusion of Sobolev spaces is compact

I know that the inclusion of Sobolev spaces with compact support is a compact map. Now I wonder whether the inclusion of isotropic Sobolev spaces is compact.

My definition of the isotropic Sobolev space is the following:

$$H^{s,t} = \{u \text{ a tempered distribution on}\ \mathbb R^n|\langle x \rangle\ ^l u \in H^s\}$$