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On the projections of the multifractal packing dimension for \(q>1\)

  • Bilel SelmiEmail author
Article
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Abstract

The aim of this article is to study the behavior 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.

Keywords

Hausdorff dimension Packing dimension Projection Multifractal analysis 

Mathematics Subject Classification

28A20 28A80 

Notes

Acknowledgements

The author is greatly indebted to the referee for carefully reading the first submitted version of this paper and giving elaborate comments and valuable suggestions on revision so that the presentation can be greatly improved.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Analysis, Probability and Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of MonastirUniversity of MonastirMonastirTunisia

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