Extensions of Rubio de Francia's extrapolation theorem.

Título inglés	Extensions of Rubio de Francia's extrapolation theorem.
Título español	Extensiones del teorema de extrapolación de Rubio de Francia.
Autor/es	Cruz-Uribe, David ; Martell, José María ; Pérez, Carlos
Organización	Dep. Math. Trinity College, Hartford (Connecticut), Estados Unidos;Dep. Mat. Univ. Autón. Madrid, Madrid, España;Dep. Anal. Mat. Fac. Mat. Univ. Sevilla, Sevilla, España
Revista	0010-0757
Publicación	2006, 57 (Extra): 195-231, 48 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	One of the main results in modern harmonic analysis is the extrapolation theorem of J. L. Rubio de Francia for Ap weights. In this paper we discuss some recent extensions of this result. We present a new approach that, among other things, allows us to obtain estimates in rearrangement-invariant Banach function spaces as well as weighted modular inequalities. We also extend this extrapolation technique to the context of A∞ weights. We apply the obtained results to the dyadic square function. Fractional integrals, singular integral operators and their commutators with bounded mean oscillation functions are also considered. We present an extension of the classical results of Boyd and Lorentz-Shimogaki to a wider class of operators and also to weighted and vector-valued estimates. Finally, the same kind of ideas leads us to extrapolate within the context of an appropriate class of non A∞ weights and this can be used to prove a conjecture proposed by E. Sawyer.
Clasificación UNESCO	120213
Palabras clave español	Análisis de Fourier ; Integrales singulares ; Operadores maximales ; Extrapolación
Código MathReviews	MR2264210
Código Z-Math	Zbl pre05077073
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