Interpolation and extrapolation of smooth functions by linear operators

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Let Cm,1(ℝn) be the space of functions on ℝn whose mth derivatives are Lipschitz 1. For E ⊂ ℝn, let Cm,1(E) be the space of all restrictions to E of functions in Cm,1(ℝn). We show that there exists a bounded linear operator T: Cm,1(E) → C m,1(ℝn) such that, for any f εC m,1(E), we have Tf= f on E.

Original languageEnglish (US)
Pages (from-to)313-348
Number of pages36
JournalRevista Matematica Iberoamericana
Issue number1
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Linear operators
  • Whitney extension problem


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