Construction of functions with prescribed Hölder and chirp exponents

We show that the Holder exponent and the chirp exponent of a function can be precribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general, Holder and chirp exponents cannot be precribed outisde a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients ; the optimality is the direct consequence of a general method we introduce in order to obtain lower bounds on the dimension of some fractal sets.