Another extension of Orlicz‐Sobolev spaces to metric spaces

Noureddine Aïssaoui

Abstract and Applied Analysis, 2004, vol. 2004, issue 1, 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 NΦ1 is a Banach space. The relationship between NΦ1 and MΦ1 (the first extension defined in Aïssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under which NΦ1 is strictly smaller than the Orlicz space LΦ.

Date: 2004
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https://doi.org/10.1155/S1085337504309012

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:1:p:1-26

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