Multivariate multifractal formalism for simultaneous pointwise (Tuipi)i regularities
Mourad Ben Slimane, Moez Ben Abid, Ines Ben Omrane, Borhen Halouani · Applicable Analysis · 2021
Recently, a multivariate multifractal analysis for pointwise regularities based on hierarchical multiresolution quantities was developed. General bounds between the Hausdorff dimension of the intersection of single fractal sets and that of the original sets were derived. Equalities were checked for some synthetic signals that include multiplicative cascades. In this paper, we focus on the setting supplied by simultaneous pointwise (Tuipi)i=1,…,L regularities. The Tup regularity for 1≤p0,1≤pi≤∞ such that si−dti>−dpi. We therefore extend previous results where only cases (pi=∞ and si−dti>0 for all i) and (pi=∞, si=dti and ri≤ 1 for all i) for simultaneous pointwise Hölder regularities have been proved.