On the smoothness of Hölder-doubling measures

Abstract

In this paper we consider the question of whether the doubling character of a measure supported on a subset of $\RR^m$ determines the regularity of its support (in a classical sense). This problem was studied by David, Kenig and Toro for codimension 1 sets under the assumption that the support be flat. Here we study the higher codimension case and remove the flatness hypothesis.

26 pages, 1 figure