Uniform sparse bounds for discrete quadratic phase Hilbert transforms
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| Autores: | , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2017 |
| Descripción: | Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, uniformly in $\alpha \in \bT$, there is a sparse bound for the bilinear form $\inn{H^{\alpha} f}{g}$. The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse H\"older classes. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/76050 |
| Acceso en línea: | https://link.springer.com/article/10.1007/s13324-017-0195-3 https://hdl.handle.net/10669/76050 |
| Palabra clave: | Discrete analysis Quadratic phase Sparse bounds Hilbert transform 515.733 Espacios de Hilbert |