Abstract
We establish versions for fractional Orlicz-Sobolev seminorms, built upon Young
functions, of the Bourgain-Brezis-Mironescu theorem on the limit as s ->1^-, and
of the Maz'ya-Shaposhnikova theorem on the limit as s->0^-, dealing with classical
fractional Sobolev spaces. As regards the limit as s ->1^-, Young functions with
an asymptotic linear growth are also considered in connection with the space of
functions of bounded variation. Concerning the limit as s->0^+, Young functions
fulfilling the \Delta_2-condition are admissible. Indeed, counterexamples show that our
result may fail if this condition is dropped. This is a joint work with Andrea
Cianchi, Lubos Pick and Lenka Slavikova.
Anno
2021
Autori IAC
Tipo pubblicazione
Altri Autori
Angela Alberico