Mixed multifractal densities for quasi-Ahlfors vector-valued measures

TL;DR

This paper develops density estimations for vector-valued quasi-Ahlfors measures within mixed multifractal analysis, enabling precise computation of their multifractal spectra and demonstrating the sufficiency of the quasi-Ahlfors condition for analysis.

Contribution

It introduces a multifractal density for multiple measures and shows it can be accurately estimated using mixed multifractal measures, facilitating spectrum computation.

Findings

Density estimations for vector-valued quasi-Ahlfors measures are established.

The multifractal spectrum can be exactly computed using the proposed density.

Quasi-Ahlfors condition is sufficient for mixed multifractal analysis.

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.