A quantitative approach to weighted Carleson condition
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are obtained. As a consequence, some sufficient conditions for the boundedness of $\m...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/673 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/673 |
| Access Level: | acceso abierto |
| Palabra clave: | weighted Carleson condition Maximal operator bumps entropy weights Poisson integral |
| Sumario: | Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are obtained. As a consequence, some sufficient conditions for the boundedness of $\mathcal{M}$ in the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela and very recently by M. Lacey and S. Spencer for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained. |
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