The structure of sobolev extension operators

Charles Fefferman, Arie Israel, Garving K. Luli

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let Lm,p(ℝn) denote the Sobolev space of functions whose m-th derivatives lie in Lp(ℝn), and assume that p > n. For E ⊆ ℝn, denote by L m,p(E) the space of restrictions to E of functions F ε L m,p(ℝn). It is known that there exist bounded linear maps T : Lm,p(E) → Lm,p(ℝn) such that Tf = f on E for any f ε Lm,p(E). We show that T cannot have a simple form called "bounded depth".

Original languageEnglish (US)
Pages (from-to)419-429
Number of pages11
JournalRevista Matematica Iberoamericana
Volume30
Issue number2
DOIs
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Linear operators
  • Sobolev spaces
  • Whitney extension problem

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