Another extension of Orlicz-Sobolev spaces to metric spaces

Aïssaoui, Noureddine

Abstr. Appl. Anal., Tome 2004 (2004) no. 1, p. 1-26 / Harvested from Project Euclid

Résumé

We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of the $\Phi$ -modulus and $\Phi$ -capacity. The resulting space $N_{\Phi}^{1}$ is a Banach space. The relationship between $N_{\Phi}^{1}$ and $M_{\Phi}^{1}$ (the first extension defined in Aïssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under which $N_{\Phi}^{1}$ is strictly smaller than the Orlicz space $\mathbf{L}_{\Phi}$ .

Publié le : 2004-02-19
Classification: 46E35, 31B15, 28A80

@article{1078681594,
     author = {A\"\i ssaoui, Noureddine},
     title = {Another extension of Orlicz-Sobolev spaces to metric spaces},
     journal = {Abstr. Appl. Anal.},
     volume = {2004},
     number = {1},
     year = {2004},
     pages = { 1-26},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1078681594}
}

Aïssaoui, Noureddine. Another extension of Orlicz-Sobolev spaces to metric spaces. Abstr. Appl. Anal., Tome 2004 (2004) no. 1, pp.  1-26. http://gdmltest.u-ga.fr/item/1078681594/