Timeline for Integration by parts in nonlocal case

9 events

when toggle format	what		by	license	comment
Jul 23, 2019 at 14:20	vote	accept	Spal
Jul 23, 2019 at 14:02	comment	added	Mateusz Kwaśnicki		If $u$ is sufficiently regular, the equality does hold; see the "positive side" of my answer. This particular $u$ should be perfectly safe: if $N > 4 s$, then this is in $L^2$ (and hence in $H^{2s}$), and when $N \leqslant 4 s$, I believe one can approximate $u$ well by $H^{2s}$ functions. (There are alternative approaches, too.)
Jul 23, 2019 at 13:12	comment	added	Spal		That means even for good functions like $u(x)=c (1+\|x\|^2)^{-\frac{N-2s}{2}},$ the equality does not hold.
Jul 23, 2019 at 12:46	history	edited	Spal	CC BY-SA 4.0	added 6 characters in body
Jul 23, 2019 at 11:09	answer	added	Mateusz Kwaśnicki		timeline score: 1
Jul 23, 2019 at 10:40	history	edited	Spal	CC BY-SA 4.0	added 18 characters in body
Jul 23, 2019 at 10:20	history	edited	Spal	CC BY-SA 4.0	added 158 characters in body
Jul 23, 2019 at 10:05	comment	added	Mateusz Kwaśnicki		What is $D^{s,2}(\mathbb{R}^N)$? In any case, you need the integral in the right-hand side over all of $\mathbb{R}^N$.
Jul 23, 2019 at 9:59	history	asked	Spal	CC BY-SA 4.0