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 sup{|∂αE(f )(x)|: |α| m, x ∈ Rd } Cm,ε f (r+ε)m, 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. © 2011 Elsevier Inc. All rights reserved.