Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces
We obtain sharp weighted Lp estimates in the Rubio de Francia extrapolation theorem in terms of the Ap characteristic constant of the weight. Precisely, if for a given 1 < r < [infinity] the norm of a sublinear operator on Lr(w) is bounded by a function of the Ar characteristic constant of the...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2055 |
| Acceso en línea: | https://ddd.uab.cat/record/2055 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_49105_03 |
| Access Level: | acceso abierto |
| Palabra clave: | Extrapolation Sharp weighted estimates Dyadic square function Dyadic paraproduct Martingale transform Hilbert transform Beurling transform |
| Sumario: | We obtain sharp weighted Lp estimates in the Rubio de Francia extrapolation theorem in terms of the Ap characteristic constant of the weight. Precisely, if for a given 1 < r < [infinity] the norm of a sublinear operator on Lr(w) is bounded by a function of the Ar characteristic constant of the weight w, then for p > r it is bounded on Lp(v) by the same increasing function of the Ap characteristic constant of v, and for p < r it is bounded on Lp(v) by the same increasing function of the r-1/p-1 power of the Ap characteristic constant of v. For some operators these bounds are sharp, but not always. In particular, we show that they are sharp for the Hilbert, Beurling, and martingale transforms. |
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