We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C1 extension theorem by Whitney [8] to Banach spaces.
Linear Lipschitz and C1 extension operators through random projection
Di Marino S.;
2021-01-01
Abstract
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C1 extension theorem by Whitney [8] to Banach spaces.
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