The functional class of Hölder exponents of continuous function
has been completely characterized by P. Andersson, K. Daoudi, S. Jaffard,
J. Lévy-Véhel and Y. Meyer [Andersson, P.: Wavelets and
local regularity. PhD Thesis. Department of Mathematics, G\"oteborg, 1997],
[Andersson, P.: Characterization of pointwise Hölder regularity.
Appl. Comput. Harmon. Anal. {\bf 4} (1997), 429-443], [Daoudi, K.,
Lévy-Véhel J. and Meyer, Y.: Construction of continuous functions
with prescribed local regularity. Constr. Approx. {\bf 14} (1998), 349-385],
[Jaffard, S.: Functions with prescribed Hölder exponent. Appl. Comput.
Harmon. Anal. {\bf 2} (1995), 400-401]; these authors have shown that this class
exactly corresponds to that of the lower limits of the sequences
of nonnegative continuous functions. The problem of determining
whether or not the Hölder exponents of discontinuous (and even
unbounded) functions can belong to a larger class remained open
during the last decade. The main goal of our article is to show
that this is not the case: the latter Hölder exponents can also
be expressed as lower limits of sequences of continuous functions.
Our proof mainly relies on a ``wavelet-leader'' reformulation of a
nice characterization of pointwise Hölder regularity due to P.
Anderson.