The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-1,
author = {Alireza Ranjbar-Motlagh},
title = {An embedding theorem for Sobolev type functions with gradients in a Lorentz space},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {1-9},
zbl = {1176.26006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-1}
}
Alireza Ranjbar-Motlagh. An embedding theorem for Sobolev type functions with gradients in a Lorentz space. Studia Mathematica, Tome 192 (2009) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-1-1/