Sobolev inequality on $\mathbb{R}^3$

Question

I know that for $u \in H^q(\mathbb{R}^d)$ with $d>q$ we have for $p = \frac{qd}{d-q}$ that $\|u\|_p \le C \|u\|_{H^q}.$

Now, I have somewhere back in my mind that it is also in the unbounded case ( $\mathbb{R}^d$ is unbounded) sufficient to have $u \in H^q(\mathbb{R}^d)$ in order to see that

$$\|u\|_p \le C \| \nabla u\|_q.$$ Unfortunately, on wikipedia I can only find this for compactly supported functions which suggests that it only holds on $H_0^q(\Omega)$ functions with $|\Omega|<\infty.$

Does anybody know if this inequality I wrote down actually holds?

If anything is unclear, please let me know.