Extended versions of the Bourgain–Brezis–Mironescu theorems on the limit as 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 , where Young functions satisfying the and the conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.
Cite this article
Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková, On the limit as of possibly non-separable fractional Orlicz–Sobolev spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 879–899DOI 10.4171/RLM/918