Spectral calculus and Lipschitz extension for barycentric metric spaces. Mendel, M. & Naor, A. Anal. Geom. Metr. Spaces, 1:163–199, 2012.
bibtex   
@article {MN-cat0-extension,
    AUTHOR = {Mendel, M. and Naor, A.},
     TITLE = {Spectral calculus and {L}ipschitz extension for barycentric metric spaces},
   JOURNAL = {Anal. Geom. Metr. Spaces},
    VOLUME = {1},
      YEAR = {2012},
     PAGES = {163--199},
     eprint={1301.3963},
}

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