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

Authors :
Selmi, Bilel
Source :
Annali di Matematica Pura ed Applicata 2019
Publication Year :
2019

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.

Details

Database :
arXiv
Journal :
Annali di Matematica Pura ed Applicata 2019
Publication Type :
Report
Accession number :
edsarx.1901.03834
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/s10231-019-00929-7