Mixed Wavelet Leaders Multifractal Formalism in a Product of Critical Besov Spaces

• Published in: Mediterranean journal of mathematics 2017-08, Vol.14 (4), p.1-20, Article 176
• Main Authors: Ben Abid, Moez, Ben Slimane, Mourad, Ben Omrane, Ines, Halouani, Borhen
• Format: Article
• Language: English
• Subjects: Formalism; Function space; Mathematics; Mathematics and Statistics; Wavelet analysis
• ISSN: 1660-5446; 1660-5454
• DOI: 10.1007/s00009-017-0964-0

In this paper, we will prove (resp. study) the Baire generic validity of the upper-Hölder (resp. iso-Hölder) mixed wavelet leaders multifractal formalism on a product of two critical Besov spaces B t 1 m t 1 , q 1 ( R m ) × B t 2 m t 2 , q 2 ( R m ) , for t 1 , t 2 > 0 , q 1 ≤ 1 and q 2 ≤ 1 . Contrary to product spaces B t 1 s 1 , ∞ ( R m ) × B t 2 s 2 , ∞ ( 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 t 1 s 1 , ∞ ( R m ) ∩ C γ 1 ( R m ) ) × ( B t 2 s 2 , ∞ ( R m ) ∩ C γ 2 ( R m ) with 0 < γ 1 < s 1 < m t 1 and 0 < γ 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 Hölder. Nevertheless, the characterization of the upper bound of the Hölder exponent by decay conditions of local wavelet leaders suffices for our study.