Sobolev multiplication theorem I would like to know whether multiplication defines a bounded map
$$H^{1/2} \otimes H^{1/2} \to H^{-1/2}$$
dimension of the domain is $3$.
I have checked two different sources and one said that it works but the other that this map is bounded as a map 
$$H^{1/2} \otimes H^{1/2} \to H^{s}$$
where $s < -\frac{1}{2}$. That is why I am confused.
Notation: $H^{1/2} = W^{1/2, 2} = L^2_{1/2}$
I would be satissfied with a source i can rely on.

See this notes by Terry Tao. Also, Sobolev multiplication below the borderline.
