Calculus of Variations and Geometric Measure Theory

E. Bruè - S. Di Marino - F. Stra

Linear Lipschitz and $C^1$ extension operators through random projections

created by dimarino on 23 Jan 2018
modified by bruè on 25 Dec 2022


Published Paper

Inserted: 23 jan 2018
Last Updated: 25 dec 2022

Journal: Journal of Functional Analysis
Year: 2018

ArXiv: 1801.07533v1 PDF


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.