JournalsrmiVol. 21, No. 2pp. 577–688

A Generalized Sharp Whitney Theorem for Jets

  • Charles Fefferman

    Princeton University, United States
A Generalized Sharp Whitney Theorem for Jets cover

Abstract

Suppose that, for each point xx in a given subset ERnE \subset \mathbb{R}^n, we are given an mm-jet f(x)f(x) and a convex, symmetric set σ(x)\sigma(x) of mm-jets at xx. We ask whether there exist a function FCm,ω(Rn)F \in C^{m , \omega} ( \mathbb{R}^n ) and a finite constant MM, such that the mm-jet of FF at xx belongs to f(x)+Mσ(x)f ( x ) + M \sigma ( x ) for all xEx \in E. We give a necessary and sufficient condition for the existence of such F,MF , M, provided each σ(x)\sigma(x) satisfies a condition that we call "Whitney ω\omega-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