Multiplication in fractional sobolev spaces

Question

Assume that $f(t)$ belongs to $W^{s_1,2}(0,T)$ and $h(x,t)$ belongs to $W^{s_2,2}(0,T;H)$ for some $s_1,s_2<\frac12$ where $H$ is a Hilbert space. It is known that for any $s<s_1+s_2-\frac12$, $s<s_1,s_2$ that the pointwise multiplication of functions is a continuous bilinear map $W^{s_1,2}(\mathbb{R})\times W^{s_2,2}(\mathbb{R}) \rightarrow W^{s,2}(\mathbb{R})$. Does there exist such a result for product of Banach/Hilbert space-valued functions?