I define the following wheighted Sobolev spaces $$L^{2,s}(\mathbb{R}^3)=\bigg\lbrace u\bigg\int_{\mathbb{R}^3}u(x)^2(1+x^2)^s<\infty\bigg\rbrace$$ and $$H^{2,s}(\mathbb{R}^3)=\bigg\lbrace u\bigg D^\alpha u\in L^{2,s}(\mathbb{R}^3),\alpha\leq 2\bigg\rbrace$$ I know that the classical Sobolev space $H^2(\mathbb{R}^3)$ is contained in $C(\mathbb{R}^3)$ because $2>\frac{3}{2}$. Can I extend this result to the above weighted Sobolev spaces?
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Continuity is a local property: functions which are in your $L^{2,s}$ are locally in $L^2$, so functions in $H^{2,s}$ are locally in the Sobolev space $H^2(\mathbb R^3)$, thus are continuous functions (even Hölder 1/2$\epsilon$). 

