Another look at Sobolev spaces

Jean Bourgain (1) , Haïm Brezis (2) , Petru Mironescu (3)

1 IAS - Institute for Advanced Study
2 LJLL - Laboratoire Jacques-Louis Lions
3 EDPA

The standard seminorm in the space $W^{s,p}$, with $s$<$1$, does not converge, when $s$ approaches $1$, to the corresponding $W^{1,p}$ seminorm. We prove that continuity is restored provided we multiply the $W^{s,p}$ seminorm by an appropriate factor.

Mots clés: finite differences; fractional Sobolev spaces

Domaines: Analyse classique [math.CA]

Jean Bourgain, Haïm Brezis, Petru Mironescu. Another look at Sobolev spaces. 2001, pp.439-455. ⟨hal-00747692⟩