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On Lp rectangular multifractal multivariate functions

Author

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  • Ben Slimane, Mourad
  • Alzughaibi, Imtithal
  • Algahtani, Obaid

Abstract

Multifractal analysis has traditionally been based on the pointwise Hölder regularity for locally bounded functions. However, recently an extension to the rectangular pointwise regularity for multivariate locally functions has generated interest. The purpose of this paper is twofold. Firstly, we characterize in hyperbolic wavelet bases the rectangular pointwise Lipschitz regularity for multivariate functions which are non necessarily locally bounded but are locally in Lp. Secondly, we perform applications for both random and deterministic anisotropic self-affine tools for some models of textures in images and flows in turbulence. Actually, we show that fractional anisotropic Wiener field are multivariate monofractal in Lp. We then construct self-affine cascade functions that are multivariate multifractal in Lp.

Suggested Citation

  • Ben Slimane, Mourad & Alzughaibi, Imtithal & Algahtani, Obaid, 2024. "On Lp rectangular multifractal multivariate functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004521
    DOI: 10.1016/j.chaos.2024.114900
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    References listed on IDEAS

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    1. S. Davies & P. Hall, 1999. "Fractal analysis of surface roughness by using spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 3-37.
    2. Mourad Ben Slimane & Moez Ben Abid & Ines Ben Omrane & Mohamad Maamoun Turkawi, 2020. "Pointwise Rectangular Lipschitz Regularities for Fractional Brownian Sheets and Some Sierpinski Selfsimilar Functions," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    3. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
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