On the projections of the multifractal Hewitt-Stromberg dimension functions

Abstract

The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In particular, we obtain general results for the multifractal analysis of the orthogonal projections on $m$-dimensional linear subspaces of a measure $\mu$ satisfying the multifractal formalism which is based on the Hewitt-Stromberg measures.