Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. The linear dependence on the characteristic of the weight $[w]_{A_{p/2}}...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1049 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1049 |
| Access Level: | acceso abierto |
| Palabra clave: | Rubio de Francia's Littlewood--Paley square function sparse domination weighted norm inequalities |
| Sumario: | We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. The linear dependence on the characteristic of the weight $[w]_{A_{p/2}}$ turns out to be sharp for $3\le p<\infty$, whereas the sharpness in the range $2<p<3$ remains as an open question. Weighted weak-type estimates in the endpoint $p=2$ are also provided. The results arise as a consequence of a sparse domination shown for these operators, obtained by suitably adapting the ideas coming from Benea [2015] and Culiuc et al. [2018]. |
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