On the Fractional Fractal Analysis of Multivariate Pointwise Lipschitz Oscillating Regularity

Authors

Ines Ben Omrane, Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi ArabiaFollow

Abstract

Classical Lipschitz regularity does not allow to capture possible different oscillating directional pointwise regularity behaviors in coordinate axes of functions f on Rd, d ≥ 2. To overcome this drawback, we use iterated fractional primitives to introduce a notion of multivariate pointwise Lipschitz oscillating regularity. We show a characterization in hyperbolic wavelet bases. As an application, we obtain the fractal print dimension of a given set of multivariate Lipschitz oscillating regularity, from the knowledge of fractional axes oscillating spaces to which f belongs.

Recommended Citation

Ben Omrane, Ines (2023) "On the Fractional Fractal Analysis of Multivariate Pointwise Lipschitz Oscillating Regularity," Information Sciences Letters: Vol. 12 : Iss. 6 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol12/iss6/2