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In this work we generalize the spaces T^{p}_{u} introduced by Calder\'on andZygmund using a pointwise version of conditions defining the generalized Besovspaces and give conditions binding the functions belonging to these spaces andthe wavelet coefficients of such functions. Next, we propose a multifractalformalism based on the new spaces wich generalize the so-called wavelet leadersmethod and show that it is satisfied on a prevalent set.

Generalized spaces of pointwise regularity: To a general framework for the WLM