%0 Journal Article
%T Spectral calculus and Lipschitz extension for barycentric metric spaces
%A Manor Mendel
%A Assaf Naor
%J Mathematics
%D 2013
%I arXiv
%R 10.2478/agms-2013-0003
%X The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT(0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.
%U http://arxiv.org/abs/1301.3963v2