While reading some articles, I found the following definition of tensor product of Sobolev spaces.
Let $d$ denotes the dimension of the domain, $s=(s_1,\dots,s_d)\in\mathbb{N}^d$. We define
$$ H^s((0,1)^d):=H^{s_1}(0,1)\otimes\dots\otimes H^{s_d}(0,1), $$ where for every $j=2,\dots,d$,
$$ H^{(s_1,\dots,s_j)}((0,1)^j):=H^{(s_1,\dots,s_{j-1})}((0,1)^{j-1})\otimes H^{s_j}(0,1)\cong H^{(s_1,\dots,s_{j-1})}((0,1)^{j-1}; H^{s_j}(0,1)). $$ It is a Hilbert space endowed with the norm $$ \|f\|^2:=\sum_{r_1=0}^{s_1}\dots\sum_{r_d=0}^{s_d}\big|\big|\frac{\partial^{r_1}\dots\partial^{r_d}f}{\partial x_1^{r_1}\dots\partial x_d^{r_d}} \big|\big|_{L^2(0,1)}^2. $$
Now, in a simple case where $s=(1,1)$, according to the definition above,
$$ H^{(1,1)}((0,1)^2):=H^1(0,1)\otimes H^1(0,1)\cong H^1((0,1); H^1(0,1)). $$
Have you ever seen anything similar?