I am looking for a reference on the paper on compact Sobolev embeddings.
If we define the Sobolev space $$X_{0}(A):=\{u\in H^s(\mathbb R^N): u=0\quad \text{in}\quad \mathbb R^N \setminus A\}$$ where $A$ is an annulus.

Is it true that the class of radial functions in $X_{0}(A)$ is compact in $L^p(A)$ for any $p>1?$