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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:

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

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