MIXED MULTIFRACTAL DENSITIES FOR QUASI-AHLFORS VECTOR-VALUED MEASURES

Anouar Ben Mabrouk and Adel Farhat ()
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Anouar Ben Mabrouk: Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Street of Assad Ibn Alfourat, Kairouan 3100, Tunisia†Laboratory of Algebra, Number Theory and Nonlinear Analysis LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, 5000 Monastir, Tunisia‡Department of Mathematics, Faculty of Sciences, University of Tabuk, Kingdom of Saudi Arabia
Adel Farhat: ��Laboratory of Algebra, Number Theory and Nonlinear Analysis LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, 5000 Monastir, Tunisia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

Abstract: In this work, some density estimations associated to vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea reposes on the fact that being quasi-Ahlfors is sufficient to conduct a mixed multifractal analysis for vector-valued measures. In this work, we introduced a multifractal density for finitely many measures, and showed that such density may be estimated well by means of the mixed multifractal measures. Such estimation induces an exact computation of multifractal spectrum of the vector-valued quasi-Ahlfors measure.

Keywords: Hausdorff Measure and Dimension; Packing Measure and Dimension; Multifractal Densities; Multifractal Formalism; Hölderian Measures; Ahlfors Measures; Mixed Cases (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400035

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DOI: 10.1142/S0218348X22400035

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