Radial extensions in fractional Sobolev spaces

Haim Brezis, Petru Mironescu, Itai Shafrir

Given $f:\partial (-1,1{)}^n\to \mathbb{R}$, consider its radial extension $Tf(X):=f(X/\Vert X{\Vert }_{\infty })$, $\forall X\in [-1,1{]}^n\setminus \{0\}$. In "On some questions of topology fo…