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January 2006 Variable exponent Sobolev spaces on metric measure spaces
Petteri Harjulehto, Peter Hästö, Mikko Pere
Funct. Approx. Comment. Math. 36: 79-94 (January 2006). DOI: 10.7169/facm/1229616443


In this article we study variable exponent Sobolev spaces on metric measure spaces. We employ two definitions: a Hajłasz type definition, which uses a pointwise maximal inequality, and a Newtonian type definition, which uses an upper gradient. We prove that these spaces are Banach, that Lipschitz functions are dense as well as other basic properties. We also study when these spaces coincide.


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Petteri Harjulehto. Peter Hästö. Mikko Pere. "Variable exponent Sobolev spaces on metric measure spaces." Funct. Approx. Comment. Math. 36 79 - 94, January 2006.


Published: January 2006
First available in Project Euclid: 18 December 2008

zbMATH: 1140.46013
MathSciNet: MR2296640
Digital Object Identifier: 10.7169/facm/1229616443

Primary: 46E35

Keywords: Hajłasz space , metric measure space , Newtonian space , Sobolev space , ‎variable exponent

Rights: Copyright © 2006 Adam Mickiewicz University

Vol.36 • January 2006
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