FINITE FRACTAL DIMENSION AND HOLDER-LIPSCHITZ PARAMETRIZATION

In this paper we first extend the Holder-Mane Theorem [1] from a finit e dimensional space to the general Hilbert space setting. Namely, if H is a real Hilbert space and X subset of or equal to H has fractal dim ension less than m/2, then for any orthogonal projection P of rank m a nd delta is an element of (0, 1) there is an orthogonal projection (P) over tilde such that parallel to P-(P) over tilde parallel to < delta and (P) over tilde \(X) has Holder inverse. Moreover, for any metric space M of finite fractal dimension less than m/2 there exists a Lipsc hitz function g:H --> R(m) with Holder inverse on its image.