Multivariate wavelet leaders Rényi dimension and multifractal formalism in mixed Besov spaces.

Ben Abid, Moez; Ben Slimane, Mourad; Ben Omrane, Ines; Turkawi, Maamoun

In this paper, we first establish a general lower bound for the multivariate wavelet leaders Rényi dimension valid for any pair (f 1 , f 2) of functions on ℝ m where f 1 belongs to the Besov space B t 1 s 1 , ∞ (ℝ m) with s 1 > m t 1 and f 2 belongs to B t 2 s 2 , ∞ (ℝ m) ∩ C γ (ℝ m) with 0 < γ < 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 Hölder spectra for all pairs (f 1 , f 2) in the same G δ -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.

BESOV spaces; MULTIFRACTALS

International Journal of Wavelets, Multiresolution & Information Processing, 2022, Vol 20, Issue 2, p1

0219-6913

Academic Journal

10.1142/S0219691321500478