A Wavelet Characterization for the Upper Global H?lder Index

摘要

The upper H?lder index has been introduced to describe smoothness properties of a continuous function. It can be seen as the irregular counterpart of the usual H?lder index and has been used to investigate the behavior at the origin of the modulus of smoothness in many classical cases. In this paper, we prove a characterization of the upper H?lder index in terms of wavelet coefficients. This result is a first step in the estimation of this exponent using wavelet methods.