Another extension of Orlicz-Sobolev spaces to metric spaces

Noureddine Aïssaoui

Abstract and Applied Analysis, 2004, vol. 2004, 1-26

Abstract:

We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of the Φ -modulus and Φ -capacity. The resulting space N Φ 1 is a Banach space. The relationship between N Φ 1 and M Φ 1 (the first extension defined in Aïssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under which N Φ 1 is strictly smaller than the Orlicz space L Φ .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:203235

DOI: 10.1155/S1085337504309012

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