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On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide

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Abstract

In this paper, we attain the multifractal Hewitt–Stromberg dimension functions of Moran measures associated with homogeneous Moran fractals and show that the multifractal Hewitt–Stromberg measures are mutually singular for which the multifractal functions do not necessarily coincide. In particular, we give a positive answer to questions posed in Attia and Selmi (J Geom Anal 31:825-862, 2021) and discuss some interesting examples.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions that led to the improvement of the manuscript. The second author would like to thank Professors Lars Olsen and Jinjun Li for useful discussions while writing this manuscript. This work is supported by Analysis, Probability & Fractals Laboratory (No: LR18ES17).

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Authors and Affiliations

  1. Analysis, Probability & Fractals Laboratory: LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000, Monastir, Tunisia

    Zied Douzi & Bilel Selmi

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  1. Zied Douzi
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  2. Bilel Selmi
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Correspondence to Zied Douzi.

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Douzi, Z., Selmi, B. On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide. Ricerche mat 72, 1–32 (2023). https://doi.org/10.1007/s11587-021-00572-6

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  • DOI: https://doi.org/10.1007/s11587-021-00572-6

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