Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 203235 | https://doi.org/10.1155/S1085337504309012

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

Received12 May 2003

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.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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