A note on Hajłasz–Sobolev spaces on fractals

We introduce Hajłasz–Sobolev spaces involving walk dimensions on subsets of Rn that will generally be fractals. The relationship between this kind of new space and the Besov space of Jonsson and Wallin is investigated. The (compact) embedding theorems for Hajłasz–Sobolev spaces are obtained.  2003 Elsevier Science (USA). All rights reserved.