I'm reading a paper and the authors applied the following sobolev type estimates $$ ||(Dv)^{2}||_{H^{3k-2}(\Omega)}\leq C||v||_{H^{3k-1+\alpha}(\Omega)}^{2} $$ for $\alpha>\frac{1}{4}$, where $v$ is a $n$ velocity vector field, $\Omega\in \mathbb{R^{n}}$ and $k$ is chosen such that $3k\geq \frac{n+3}{2}$.
I was wondering if anyone has seen this inequality before and can provide me one of its reference? I couldn't find the exact inequality applies to it. The closest one should be general sobolev embedding but its condition involves dimension $n$ so doesn't work.