Abstract
In this paper, we will prove (resp. study) the Baire generic validity of the upper-Holder (resp. iso-Holder) mixed wavelet leaders multif-ractal formalism on a product of two critical Besov spaces B-t1(m/t1,q1) (R-m) x B-t2(m/t2,q2) (R-m), for t(1), t(2) > 0, q(1) <= 1 and q(2) <= 1. Contrary to product spaces B-t1(s1,infinity) (R-m) x B-t2(s2,infinity) (R-m) with s(1) > m/t(1) and s(2) > m/t(2) (Ben Slimane in Mediterr J Math, 13(4): 1513-1533, 2016) and (B-t1(s1,infinity) (R-m) boolean AND C-gamma 1 (R-m)) x (B-t2(s2,infinity) (R-m) boolean AND C-gamma 2 (R-m) with 0 < gamma(1) < s(1) < m/t(1) and 0 < gamma(2) < s(2) < m/t(2) (Ben Abid et al. in Mediterr J Math, 13(6):5093-5118, 2016), all pairs of functions in the obtained generic set are not uniform Holder. Nevertheless, the characterization of the upper bound of the Holder exponent by decay conditions of local wavelet leaders suffices for our study.