Abstract
Recently, a large deviation multifractal formalism based on histograms of wavelet leader coefficients, compared to some other wavelet-based formalisms, was proved to be efficient for uniform Holder functions. In this paper, we extend this efficiency for non-uniform Holder functions. We first obtain optimal bounds for both wavelet and wavelet leader histograms for all functions in the critical Besov space Btm/t,q(T), where t,q>0 and T is the unit torus of Rm. We then compute these histograms for quasi-all functions in Btm/t,q(T), in the sense of Baire Category. Although, increasing parts of these histograms have increasing visibility, they coincide only if 0<qt. If moreover q1, then wavelet leader histograms method covers the Holder spectrum for all t>0, however wavelet histograms method covers it only if 0<qt.