Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
So you're basically using that the operator $(1 - \Delta)^{r/2}$ (defined by some functional calculus I suppose) is an isometry between $W^r$ and $L^2$?
Oh I think I understand now, $g$ is defined on a set larger than $B$... So you just integrate f twice in every direction on $B$ and then fix everything outside $B$ so that the support is compact
In Step 5, how do you know that $\partial^{(2, \dots, 2)}$ can be an arbitrary test function? E.g. for $n=1$ a positive function can't be the second derivative of a compactly supported function, right?
@MateuszKwaśnicki Also, what kind of integral are you talking about for $n \geq 2$? I wouldn't know how to take line integrals of a measure (and I actually doubt its possible?)
@MateuszKwaśnicki it's definitely not quite that easy because $\operatorname{sign}' = 2\delta_0$ is of order zero but maybe integrating twice can work...
