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Another extension of Orlicz-Sobolev spaces to metric spaces

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  • Noureddine Aïssaoui

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 .

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  • Noureddine Aïssaoui, 2004. "Another extension of Orlicz-Sobolev spaces to metric spaces," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-26, January.
    • Handle: RePEc:hin:jnlaaa:203235
    DOI: 10.1155/S1085337504309012
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