Whitney extension operators without loss of derivatives

• Leonhard Frerick ^[1] ; Enrique Jordá ^[2] ; Jochen Wengenroth ^[1]
  1. [1] University of Trier

     University of Trier

     Kreisfreie Stadt Trier, Alemania

     
  2. [2] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 377-390
• Idioma: inglés
• DOI: 10.4171/RMI/888
• Texto completo no disponible (Saber más ...)
• Resumen

  • For a compact set K⊆Rd we characterize the existence of a linear extension operator E:E(K)→C∞(Rd) for the space of Whitney jets E(K) without loss of derivatives, that is, it satisfies the best possible continuity estimates sup{|∂αE(f)(x)|:|α|≤n,x∈Rd}≤Cn∥f∥n, where ∥⋅∥n denotes the nn-th Whitney norm. The characterization is by a surprisingly simple purely geometric condition introduced by Jonsson, Sjögren, and Wallis: there is ϱ∈(0,1) such that, for every x0∈K and ϵ∈(0,1), there are dd points x1…,xd in K∩B(x0,ϵ) satisfying dist(xn+1,\rm affine hull{x0,…,xn})≥ϱϵ for all n∈{0,…,d−1}.