On the projections of the multifractal packing dimension for q>1

Abstract

The aim of this article is to study the behaviour of the multifractal packing function $B_{\mu }(q)$ under projections in Euclidean space for $q>1$. We show that $B_{\mu }(q)$ is preserved under almost every orthogonal projection. 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.