A question on a bounded sequence in $H^1(\mathbb{R}^n)$.

Question

Let $r>0$, and $2 \le q \le 2^*$. Suppose that $\{u_k\}_k$ is a bounded sequence in $H^1(\mathbb{R}^n)$ and $\lim_{k\to \infty} \sup_{y \in \mathbb{R}^n} \int_{B_r(y)}|u_k|^q dx \rightarrow 0.$ How can I show that $u_k \rightarrow 0$ in $L^p(\mathbb{R}^n)$ for $2 < p < 2^*$?