Generalized spaces of pointwise regularity: To a general framework for the WLM

2019/10/07 by Laurent Loosveldt, Samuel Nicolay, Loosveldt, Laurent +1 · 1 citation
Computer Science · Mathematics · #26A16 #28A78 #42C40 #Advanced Data Compression Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1910.02651

openalex publication_date 2019/10/07 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we generalize the spaces T^p_u introduced by Calderón and Zygmund using a pointwise version of conditions defining the generalized Besov spaces and give conditions binding the functions belonging to these spaces and the wavelet coefficients of such functions. Next, we propose a multifractal formalism based on the new spaces wich generalize the so-called wavelet leaders method and show that it is satisfied on a prevalent set.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.
• Orthonormal bases of compactly supported wavelets

Cited by

• The p-spectrum of Random Wavelet Series

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