Open Access
April, 2007 The Structure of Linear Extension Operators for $C^m$
Charles Fefferman
Rev. Mat. Iberoamericana 23(1): 269-280 (April, 2007).


For any subset $E \subset \mathbb{R}^n$, let $C^m (E)$ denote the Banach space of restrictions to $E$ of functions $F \in C^m (\mathbb{R}^n)$. It is known that there exist bounded linear maps $T:C^m(E)\longrightarrow C^m(\mathbb{R}^n)$ such that $Tf = f$ on $E$ for any $f \in C^m (E)$. We show that $T$ can be taken to have a simple form, but cannot be taken to have an even simpler form.


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Charles Fefferman. "The Structure of Linear Extension Operators for $C^m$." Rev. Mat. Iberoamericana 23 (1) 269 - 280, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1120.41002
MathSciNet: MR2351135

Primary: 41A05 , 41A45

Keywords: extension operators , Whitney's extension problem

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 1 • April, 2007
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