Definitions of Sobolev classes on metric spaces

Authors
Franchi, B Hajlasz, P Koskela, P
Citation
B. Franchi et al., Definitions of Sobolev classes on metric spaces, ANN I FOUR, 49(6), 1999, pp. 1903
Citations number
22
Categorie Soggetti
Mathematics
Journal title
ANNALES DE L INSTITUT FOURIER
ISSN journal
03730956 → ACNP
Volume
49
Issue
6
Year of publication
1999
Database
ISI
SICI code
0373-0956(1999)49:6<1903:DOSCOM>2.0.ZU;2-5
Abstract
There have been recent attempts to develop the theory of Sobolev spaces W-1 .p on metric spaces that do not admit any differentiable structure. We prov e that certain definitions are equivalent. We also define the spaces in the limiting case p = 1.