On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces (Q2039127)

Summary: Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as \(s\to 1^-\) 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 [\textit{J.~Fernández Bonder} and \textit{A.~M. Salort}, J. Funct. Anal. 277, No.~2, 333--367 (2019; Zbl 1426.46018)], where Young functions satisfying the \(\Delta_2\) and the \(\nabla_2\) 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.