Resumen de Fuglede’s theorem in generalized Orlicz–Sobolev spaces

Jonne Juusti

• In this paper, we show that Orlicz–Sobolev spaces W1,φ(Ω) can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that C1(Ω) functions are dense in W1,φ(Ω), and φ(x,β)≥1 for some β>0 and almost every x∈Ω. The results are new even in the special cases of Orlicz and double phase growth.