Variable exponent Sobolev spaces on metric measure spaces
Authors:
- Petteri HarjulehtoPHPetteri Harjulehto
- Peter HästöPHPeter Hästö
- Mikko PereMPMikko Pere
Open Access
- 1 January 2006
- journal article
- Published by Adam Mickiewicz University (Euclid) in Functiones et Approximatio Commentarii Mathematici
- Vol. 36 (none) , 79-94
Abstract
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.Keywords
This publication has 23 references indexed in Scilit:
- Integral operators on the halfspace in generalized Lebesgue spaces , part IJournal of Mathematical Analysis and Applications, 2004
- Maximal and Fractional Operators in Weighted $L^{p(x)}$ SpacesRevista Matemática Iberoamericana, 2004
- Continuity of Sobolev functions of variable exponent on metric spacesProceedings of the Japan Academy, Series A, Mathematical Sciences, 2004
- On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω)Journal of Mathematical Analysis and Applications, 2001
- An example of a space Lp(x) on which the Hardy-Littlewood maximal operator is not boundedExpositiones Mathematicae, 2001
- Newtonian spaces: An extension of Sobolev spaces to metric measure spacesRevista Matemática Iberoamericana, 2000
- Hölder quasicontinuity of Sobolev functions on metric spacesRevista Matemática Iberoamericana, 1998
- Density of smooth functions in Wk, p(x) ( Ω )Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Topology of the space ? p(t) ([0, 1])Mathematical Notes, 1979
- Extension of range of functionsBulletin of the American Mathematical Society, 1934