Fuglede's theorem in generalized Orlicz-Sobolev spaces

Abstract

In this paper, we show that Orlicz-Sobolev spaces W-1,W-phi(Omega) 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(Omega) functions are dense in W-1,W-phi(Omega), and phi(x, beta) >= 1 for some beta > 0 and almost every x epsilon Omega. The results are new even in the special cases of Orlicz and double phase growth.