Mollification fractional Sobolev function(Convergence) I got a function $u\in W^{\frac{3}{2},2}((0,1),\mathbb{R}^n)$ and a standard mollifier $\eta_\epsilon$. It follows that the mollification $u_\epsilon$ converges to $u$ in $W^{\frac{3}{2},2}((0,1),\mathbb{R}^n)$. My problem is the semi-norm of $u'$, it is rather clear that $u_\epsilon \to u$ in $W^{1,2}((0,1),\mathbb{R}^n)$ Does anyone know a good reference to a proof?

I found a nice reference, they solved the problem in a more universal setting
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Lemma 11