A Fefferman-Stein inequality for the Carleson operator
We provide a Fefferman-Stein type weighted inequality for maximally modulated Calderón-Zygmund operators that satisfy a priori weak type unweighted estimates. This inequality corresponds to a maximally modulated version of a result of Pérez. Applying it to the Hilbert transform we obtain the corresp...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1742 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1742 |
| Access Level: | acceso abierto |
| Palabra clave: | Carleson operator Maximal operators Sparse operators Weighted inequality |
| Sumario: | We provide a Fefferman-Stein type weighted inequality for maximally modulated Calderón-Zygmund operators that satisfy a priori weak type unweighted estimates. This inequality corresponds to a maximally modulated version of a result of Pérez. Applying it to the Hilbert transform we obtain the corresponding inequality for the Carleson operator C, that is C : Lp(Mp+1w) → Lp(w) for any 1 < p < ∞ and any weight function w, with bound independent of w. We also provide a maximalmultiplier weighted theorem, a vector-valued extension, and more general two-weighted inequalities. Our proof builds on a recent work of Di Plinio and Lerner combined with some results on Orlicz spaces developed by Pérez. |
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