Weighted integrability of Sobolev functions in $H^2_p$

Question

Suppose $u \in H^2_p(\mathbb{R}^n)$. What can be said about the decay of $u$ in an $L^p(\mathbb{R}^n)$ sense, i.e. is it true that $$\int_{\mathbb{R}^n} |xu(x)|^pdx < \infty?$$