Sobolev type spaces on metric measure spaces. (English) Zbl 1120.31004

Aikawa, Hiroaki (ed.) et al., Potential theory in Matsue. Selected papers of the international workshop on potential theory, Matsue, Japan, August 23–28, 2004. Tokyo: Mathematical Society of Japan (ISBN 4-931469-33-7/hbk). Advanced Studies in Pure Mathematics 44, 77-90 (2006).
Some of the approaches to extending Sobolev space theory to metric measure spaces are described. In particular, the Hajłasz-Sobolev, Newton-Sobolev, and the Korevaar-Schoen type Sobolev spaces, and the connections between them, are considered.
No proofs are provided but the references are given.
For the entire collection see [Zbl 1102.31001].


31C45 Other generalizations (nonlinear potential theory, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems