# Some examples of $C^\infty$ extension by linear operators

### Charles Fefferman

Princeton University, United States### Fulvio Ricci

Scuola Normale Superiore, Pisa, Italy

## Abstract

For two kinds of sets $X$ in $\mathbb{R}^n$, we prove the existence of linear continuous operators extending $C^\infty$ functions on $X$ to $C^\infty$ functions on $\mathbb{R}^n$. The sets we consider are: (a) sequences of points in the real line converging to 0 at a polynomial rate, (b) flag-shaped sets in the plane, which are unions of half-lines with slopes as in (a).

## Cite this article

Charles Fefferman, Fulvio Ricci, Some examples of $C^\infty$ extension by linear operators. Rev. Mat. Iberoam. 28 (2012), no. 1, pp. 297–304

DOI 10.4171/RMI/678