Mixed multifractal densities for quasi-Ahlfors vector-valued measures

Abstract

In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient to conduct a mixed multifractal analysis for vector-valued measures. In the present 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 the multifractal spectrum of the vector-valued quasi-Ahlfors measure.

arXiv comment23 pages

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• Packing dimension and Ahlfors regularity of porous sets in metric spaces
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• Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches