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.
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