Noureddine Aïssaoui, "Another extension of Orlicz-Sobolev spaces to metric spaces", Abstract and Applied Analysis, vol. 2004, Article ID 203235, 26 pages, 2004. https://doi.org/10.1155/S1085337504309012
Another extension of Orlicz-Sobolev spaces to metric spaces
We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of the -modulus and -capacity. The resulting space is a Banach space. The relationship between and (the first extension defined in Aïssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under which is strictly smaller than the Orlicz space .
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