- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
16
2000
2
Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
Nageswari
Shanmugalingam
University of Cincinnati, CINCINNATI, UNITED STATES
This paper studies a possible de finition of Sobolev spaces in abstract metric spaces and answers in the affi rmative the question whether this defi nition yields a Banach space. The paper also explores the relationship between this defi nition and the Haj lasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven . Diff erent versions of capacities are also explored and these various def initions are compared. The main tool used in this paper is the concept of moduli of path families .
General
243
279
10.4171/RMI/275
http://www.ems-ph.org/doi/10.4171/RMI/275