JournalsrmiVol. 21, No. 1pp. 313–348

Interpolation and extrapolation of smooth functions by linear operators

  • Charles Fefferman

    Princeton University, United States
Interpolation and extrapolation of smooth functions by linear operators cover
Download PDF

Abstract

Let Cm,1(Rn)C^{m , 1} ( \mathbb{R}^n) be the space of functions on Rn\mathbb{R}^n whose mthm^{\sf th} derivatives are Lipschitz 1. For ERnE \subset \mathbb{R}^n, let Cm,1(E)C^{m , 1} (E) be the space of all restrictions to EE of functions in Cm,1(Rn)C^{m,1} ( \mathbb{R}^n). We show that there exists a bounded linear operator T:Cm,1(E)Cm,1(Rn)T: C^{m , 1} (E) \rightarrow C^{m , 1} ( \mathbb{R}^n) such that, for any fCm,1(E)f \in C^{m , 1} ( E ), we have Tf=fT f = f on EE.

Cite this article

Charles Fefferman, Interpolation and extrapolation of smooth functions by linear operators. Rev. Mat. Iberoam. 21 (2005), no. 1, pp. 313–348

DOI 10.4171/RMI/424