This is an announcement for the paper “Linear Lipschitz and $C^1$ extension operators through random projection” by Elia Bruèhttps://arxiv.org/find/math/1/au:+Brue_E/0/1/0/all/0/1, Simone Di Marinohttps://arxiv.org/find/math/1/au:+Marino_S/0/1/0/all/0/1, Federico Strahttps://arxiv.org/find/math/1/au:+Stra_F/0/1/0/all/0/1.

Abstract: We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$ extension theorem by Whitney to Banach spaces.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.07533