Haar wavelet characterization of dyadic Lipschitz regularity
Autor: | Aimar, Hugo, Arias, Carlos Exequiel, Gómez, Ivana |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.33044/revuma.3574 |
Popis: | We obtain a necessary and sufficient condition on the Haar coefficients of a real function $f$ defined on $\mathbb{R}^+$ for the Lipschitz $\alpha$ regularity of $f$ with respect to the ultrametric $\delta(x,y)=\inf \{|I|: x, y\in I; I\in\mathcal{D}\}$, where $\mathcal{D}$ is the family of all dyadic intervals in $\mathbb{R}^+$ and $\alpha$ is positive. Precisely, $f\in \textrm{Lip}_\delta(\alpha)$ if and only if $\left\vert\left Comment: 6 pages. This manuscript has been accepted for publication in the Revista de la Uni\'{o}n Matem\'{a}tica Argentina |
Databáze: | arXiv |
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