Multivariate wavelet leaders Renyi dimension and multifractal formalism in mixed Besov spaces

In this paper, we first establish a general lower bound for the multivariate wavelet leaders Renyi dimension valid for any pair (f(1), f(2)) of functions on R-m where f(1) belongs to the Besov space B-t1(s1,)infinity (R-m) with s(1) > m/t(1) and f(2) belongs to B-t2(s2,)infinity (R-m) boolean AND C-gamma (R-m) with 0 < gamma < s(2) < m/t(2). We then prove the optimality of this result for quasi all pairs (f(1), f(2)) in the Baire generic sense. Finally, we compute both iso-mixed and upper-multivariate Holder spectra for all pairs (f(1), f(2)) in the same G(delta)-set. This allows to prove (respectively, study) the Baire generic validity of the upper-multivariate (respectively, iso-multivariate) multifractal formalism based on wavelet leaders for such pairs.