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

Jonne Juusti

• In this paper, we show that Orlicz–Sobolev spaces W^{1,\varphi }(\varOmega ) 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 C^1(\varOmega ) functions are dense in W^{1,\varphi }(\varOmega ), and \varphi (x,\beta ) \ge 1 for some \beta > 0 and almost every x \in \varOmega. The results are new even in the special cases of Orlicz and double phase growth.