# A Generalized Sharp Whitney Theorem for Jets

### Charles Fefferman

Princeton University, United States

## Abstract

Suppose that, for each point $x$ in a given subset $E⊂R_{n}$, we are given an $m$-jet $f(x)$ and a convex, symmetric set $σ(x)$ of $m$-jets at $x$. We ask whether there exist a function $F∈C_{m,ω}(R_{n})$ and a finite constant $M$, such that the $m$-jet of $F$ at $x$ belongs to $f(x)+Mσ(x)$ for all $x∈E$. We give a necessary and sufficient condition for the existence of such $F,M$, provided each $σ(x)$ satisfies a condition that we call "Whitney $ω$-convexity''.

## Cite this article

Charles Fefferman, A Generalized Sharp Whitney Theorem for Jets. Rev. Mat. Iberoam. 21 (2005), no. 2, pp. 577–688

DOI 10.4171/RMI/430