Two results concerning chirps and 2-microlocal exponents prescription

Abstract : The local behavior of a function near a Hölder singularity located at a point x_0 can be finely described by means of its 2-microlocal domain. We solve the issue of prescribing this domain. A more compact description can be given using two parameters, the Hölder exponent and the chirp exponent. We give a necessary condition satisfied by this couple of exponents considered as functions of x_0.