Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - D. Puglisi

Linear extension operators between spaces of Lipschitz maps and Optimal Transport}

created by ambrosio on 02 Sep 2016
modified on 07 Sep 2016

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Submitted Paper

Inserted: 2 sep 2016
Last Updated: 7 sep 2016

Year: 2016

Abstract:

Motivated by the notion of $K$-gentle partition of unity introduced by Lee-Naor and by the notion of $K$-Lipschitz retract studied by S.Ohta, we study a weaker notion related to the Kantorovich-Rubinstein transport distance, that we call $K$-random projection. We show that $K$-random projections can still be used to provide linear extension operators for Lipschitz maps. We also prove that the existence of these random projections is necessary and sufficient for the existence of weak$^*$ continuous operators. Finally we use this notion to characterize the metric spaces $(X,d)$ such that the free space $\mathcal{F}(X)$ has the bounded approximation propriety.


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