Resumen de A Generalized Sharp Whitney Theorem for Jets

Charles L. Fefferman

• Suppose that, for each point x in a given subset E Ì Rn, we are given an m-jet f(x) and a convex, symmetric set ?(x) of m-jets at x. We ask whether there exist a function F Î Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + M?(x) for all x Î E. We give a necessary and sufficient condition for the existence of such F, M, provided each ?(x) satisfies a condition that we call "Whitnet w-convexity".