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DurandCartagena, Estibalitz (2013) First order Poincaré inequalities in metric measure spaces. Annales academiae scientiarum fennicaemathematica, 38 (1). pp. 287308. ISSN 1239629X

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Official URL: http://www.acadsci.fi/mathematica/Vol38/vol38pp287308.pdf
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Abstract
We study a generalization of classical Poincare inequalities, and study conditions that link such an inequality with the first order calculus of functions in the metric measure space setting when the measure is doubling and the metric is complete. The first order calculus considered in this paper is based on the approach of the upper gradient notion of Heinonen and Koskela [HeKo]. We show that under a Vitali type condition on the BMOPoincare type inequality of Franchi, Perez and Wheeden [FPW], the metric measure space should also support a pPoincare inequality for some 1 <= p < infinity, and that under weaker assumptions, the metric measure space supports an infinityPoincare inequality in the sense of [DJS].
Item Type:  Article 

Uncontrolled Keywords:  Poincare inequality; BMOPoincare inequality; quasiconvexity; Lipschitz functions; Newtonian functions; thick quasiconvexity 
Subjects:  Sciences > Mathematics > Functions Sciences > Mathematics 
ID Code:  21226 
Deposited On:  06 May 2013 11:09 
Last Modified:  07 Feb 2014 10:27 
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