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Integral inequalities involving generalized Erdélyi-Kober fractional integral operators

Dumitru Baleanu, Sunil Dutt Purohit, Jyotindra C. Prajapati (2016)

Open Mathematics

Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.

Inverse Limit Spaces Satisfying a Poincaré Inequality

Jeff Cheeger, Bruce Kleiner (2015)

Analysis and Geometry in Metric Spaces

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces,...

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