Definitions of Sobolev classes on metric spaces

Bruno Franchi, Piotr Hajlasz, and Pekka Koskela

Contact the author: Please use for correspondence this email.
Submission date: 28. Feb. 1998
Pages: 25
published in: Annales de l'Institut Fourier, 49 (1999) 6, p. 1903-1924 
Bibtex
Download full preprint: PDF (453 kB), PS ziped (172 kB)

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 prove that certain definitions are equivalent. We also define the spaces in the limiting case p=1.