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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2306.05015 |
| Etiquetas: |
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- Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure $μ$ vanishes, then the set of points where the principal value of the Cauchy singular integral of $μ$ exists has Hausdorff dimension 1. The result is extended to Cantor sets in $\mathbb{R}^d$ of Hausdorff dimension $α$ and Riesz singular integrals of homogeneity $-α$, 0 < $α$ < d : the set of points where the principal value of the Riesz singular integral of $μ$ exists has Hausdorff dimension $α$. A martingale associated with the singular integral is introduced to support the proof.