Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 1-26

Another extension of Orlicz-Sobolev spaces to metric spaces

Noureddine Aïssaoui

Département de Mathématiques, Ecole Normale Supérieure, Ben Souda, Fés 5206, Morocco

Received 12 May 2003

Copyright © 2004 Noureddine Aïssaoui. 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.


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.