  We show the relevance of a multifractal-type analysis for pointwise
convergence and divergence properties of wavelet series: Depending on the
sequence space which the wavelet coefficients sequence belongs to, we obtain
deterministic upper bounds for the Hausdorff dimensions of the sets of points
where a given rate of divergence occurs, and we show that these bounds are
generically optimal, according to several notions of genericity.
