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...

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Detalles Bibliográficos
Autores: Cruz Uribe, David, Martell Berrocal, José María, Pérez Moreno, Carlos
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
Descripción
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.