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Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals

Opened Access Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals

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Autor: Curbera Costello, Guillermo
García Cuerva, José
Martell Berrocal, José María
Pérez Moreno, Carlos
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2006-06-20
Publicado en: Advances in Mathematics, 203 (1), 256-318.
Tipo de documento: Artículo
Resumen: We present an extrapolation theory that allows us to obtain, from weighted Lp inequalities on pairs of functions for p fixed and all A∞ weights, estimates for the same pairs on very general rearrangement invariant quasi-Banach function spaces with A∞ weights and also modular inequalities with A∞ weights. Vector-valued inequalities are obtained automatically, without the need of a Banachvalued theory. This provides a method to prove very fine estimates for a variety of operators which include singular and fractional integrals and their commutators. In particular, we obtain weighted, and vector-valued, extensions of the classical theorems of Boyd and Lorentz-Shimogaki. The key is to develop appropriate versions of Rubio de Francia’s algorithm.
Cita: Curbera Costello, G., García Cuerva, J., Martell Berrocal, J.M. y Pérez Moreno, C. (2006). Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals. Advances in Mathematics, 203 (1), 256-318.
Tamaño: 422.7Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47929

DOI: 10.1016/j.aim.2005.04.009

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