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INICIO | 19 de mayo de 2024

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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)