On the limit as s -> 1- of possibly non-separable fractional Orlicz-Sobolev spaces

Abstract

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s ! 1 of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, and complement those of [13].

Keywords

• non-separable
• fractional
• Orlicz-Sobolev
• spaces