Another look at Sobolev spaces
Bourgain, Jean ; Brezis, Haïm ; Mironescu, Petru
HAL, hal-00747692 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-05
Classification:  fractional Sobolev spaces,  finite differences,  46E35,  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] 
@article{hal-00747692,
     author = {Bourgain, Jean and Brezis, Ha\"\i m and Mironescu, Petru},
     title = {Another look at Sobolev spaces},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00747692}
}

Bourgain, Jean; Brezis, Haïm; Mironescu, Petru. Another look at Sobolev spaces. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00747692/