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March, 2009 Extension of $C^{m, \omega}$-Smooth Functions by Linear Operators
Charles Fefferman
Rev. Mat. Iberoamericana 25(1): 1-48 (March, 2009).

Abstract

Let $C^{m, \omega} ( \mathbb{R}^n)$ be the space of functions on $\mathbb{R}^n$ whose $m^{\sf th}$ derivatives have modulus of continuity $\omega$. For $E \subset \mathbb{R}^n$, let $C^{m , \omega} (E)$ be the space of all restrictions to $E$ of functions in $C^{m , \omega} ( \mathbb{R}^n)$. We show that there exists a bounded linear operator $T: C^{m , \omega} ( E ) \rightarrow C^{m , \omega } ( \mathbb{R}^n)$ such that, for any $f \in C^{m , \omega} ( E )$, we have $T f = f$ on $E$.

Citation

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Charles Fefferman . "Extension of $C^{m, \omega}$-Smooth Functions by Linear Operators." Rev. Mat. Iberoamericana 25 (1) 1 - 48, March, 2009.

Information

Published: March, 2009
First available in Project Euclid: 12 March 2009

zbMATH: 1173.46014
MathSciNet: MR2514337

Subjects:
Primary: 65D05, 65D17

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.25 • No. 1 • March, 2009
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