Sharp weighted estimates for approximating dyadic operators
We give a new proof of the sharp weighted L2 inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where T is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42344 |
| Acceso en línea: | http://hdl.handle.net/11441/42344 https://doi.org/10.3934/era.2010.17.12 |
| Access Level: | acceso abierto |
| Palabra clave: | Ap weights Haar shift operators singular integral operators Hilbert transform Riesz transforms Beurling-Ahlfors operator dyadic square function vector-valued maximal operator |
| Sumario: | We give a new proof of the sharp weighted L2 inequality ||T||_{L^2(w)} \leq c [w]_{A_2} where T is the Hilbert transform, a Riesz transform, the Beurling-Ahlfors operator or any operator that can be approximated by Haar shift operators. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. |
|---|