JournalsrmiVol. 23, No. 1pp. 269–280

The Structure of Linear Extension Operators for CmC^m

  • Charles Fefferman

    Princeton University, United States
The Structure of Linear Extension Operators for $C^m$ cover
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Abstract

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

Cite this article

Charles Fefferman, The Structure of Linear Extension Operators for CmC^m. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 269–280

DOI 10.4171/RMI/495