Tame linear extension operators for smooth Whitney functions

For a compact set K⊆Rd we present a rather easy construction of a linear extension operator E:E(K)→C∞(Rd) for the space of Whitney jets E(K) which satisfies linear tame continuity estimates , where ‖⋅‖s denotes the s-th Whitney norm. The construction turns out to be possible if and only if the local Markov inequality LMI(s) introduced by Bos and Milman holds for every s>r on K. In particular, E(K) admits a tame linear extension operator if and only if the local Markov inequality LMI(s) holds on K for some s⩾1.