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Alberico, Angela; Cianchi, Andrea; Pick, Lubos; Slavikova, Lenka
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, 12/2020, Letnik: 31, Številka: 4Journal Article
Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s right arrow 1.sup.- 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, where Young functions satisfying the DELTA.sub.2 and the nabla.sub.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. KEY WORDS: Fractional Orlicz--Sobolev spaces, limit of smoothness parameters, Orlicz--Sobolev spaces, functions of bounded variation MATHEMATICS SUBJECT CLASSIFICATION: 46E35, 46E30
