Tame linear extension operators for smooth Whitney functions |
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Authors: | Leonhard Frerick, Enrique Jord ,Jochen Wengenroth |
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Affiliation: | a Fachbereich IV – Mathematik, Universität Trier, D-54286 Trier, Germany;b Departamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Plaza Ferrándiz y Carbonell 2, E-03801 Alcoy (Alicante), Spain |
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Abstract: | 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. |
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Keywords: | Whitney jet Extension operator Markov inequality |
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