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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
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Embedding of weighted sobolev space with exponential weights
Expanding on my comment, let $u_i\in W^{2,p}_\mu(\mathbb{R}^d)$ be a bounded sequence, that is, $$
|u_i|_{W^{2,p}_\mu(\mathbb{R}^d)}\leq C
$$
and consider the balls $B_k(0)$, $k\in\mathbb{N}$. Let $W^ …