On the projections of mutual multifractal spectra

TL;DR

This paper investigates how the mutual multifractal spectrum of measures behaves under projections, establishing relationships and improving existing results in the context of Euclidean space.

Contribution

It introduces a relationship between the mutual multifractal spectra of measures and their orthogonal projections, enhancing previous findings in the field.

Findings

Established a relationship between spectra of measures and their projections

Improved Svetova's results on mutual multifractal analysis

Analyzed the behavior of measures under orthogonal projections

Abstract

The aim of this article is to study the behaviour of the relative multifractal spectrum under projections. First of all, we depict a relationship between the mutual multifractal spectra of a couple of measures $(\mu, \nu)$ and its orthogonal projections in Euclidean space. As an application, we improve Svetova's result (Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 11 (2004), 41-46) and study the mutual multifractal analysis of the projections of measures.