Product of Sobolev spaces

Question

Let $X$ and $Y$ be measure spaces. I know that $L^2(X\times Y)$ is isomorphic to $L^2(X)\otimes L^2(Y)$.

Is there a similar property for Sobolev spaces? For istance, is true that $H^2([0,1]^2)\cong H^2([0,1])\otimes H^2([0,1])$ ?

Thanks in advance.