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Dimension prints for continuous functions on the unit square

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Abstract

Recently, we have proved that the rectangular pointwise Lipschitz regularity of a continuous function on the unit square is directly related with the local suprema of the coefficients of the function in the tensor product Faber–Schauder basis. In this paper, we provide print dimension information on the distribution at all bi-scales of these local suprema. We apply our results for self-affine functions associated to the Schauder product function and a particular type of Sierpinski carpets.

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Acknowledgements

Mourad Ben Slimane thank Stéphane Jaffard for stimulating discussions.

The authors thank the referees for their comments and remarks that greatly helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Université de Sousse, Ecole Supérieure des Sciences et Technologie de Hammam Sousse, Sousse, 4011, Tunisia

    M. Ben Abid

  2. Department of Mathematics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O.Box 90950, Riyadh, 11623, Saudi Arabia

    I. Ben Omrane

  3. Department of Mathematics, College of Science, King Saud University, P.O.Box 2455, Riyadh, 11451, Saudi Arabia

    M. Ben Slimane & M. Turkawi

Authors
  1. M. Ben Abid
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  2. I. Ben Omrane
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  3. M. Ben Slimane
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  4. M. Turkawi
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Corresponding author

Correspondence to M. Ben Slimane.

Additional information

Mourad Ben Slimane and Maamoun Turkawi extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No. (RG- 1435-063).

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Ben Abid, M., Ben Omrane, I., Ben Slimane, M. et al. Dimension prints for continuous functions on the unit square. Acta Math. Hungar. 165, 78–99 (2021). https://doi.org/10.1007/s10474-021-01172-4

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  • DOI: https://doi.org/10.1007/s10474-021-01172-4

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