Fuglede’s theorem in generalized Orlicz–Sobolev spaces

• Juusti, Jonne ^[1]
  1. [1] University of Turku

     University of Turku

     Turku, Finlandia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 2, 2023, págs. 299-312
• Idioma: inglés
• DOI: 10.1007/s13348-021-00347-0
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• Resumen

  • 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.