Is $C_\mathrm{c}^\infty (\mathbb R^d \setminus \lbrace 0 \rbrace ) \subset H^{m,p}(\mathbb R^d )$ dense?

Question

The title says it:

$$C_\mathrm{c}^\infty (\mathbb R^d ) \subset H^{m,p}(\mathbb R^d )$$ is a dense subset. Is the same true if I leave out one point, i.e., is $$C_\mathrm{c}^\infty (\mathbb R^d \setminus \lbrace 0 \rbrace ) \subset H^{m,p}(\mathbb R^d )$$ dense? I expect this to depend upon $m,p,d$...