Local regularity of nonsmooth wavelet expansions and application to the Polya function

Abstract

We give criteria of pointwise regularity for expansions on Haar or Schauder basis (or spline-type wavelets) corresponding to large Hölder exponents. As an application, we determine the exact Hölder regularity of the Polya function at every point and show that it is multifractal. © 1996 Academic Press, Inc.