Extensions of Rubio de Francia's extrapolation theorem.

Cruz-Uribe, David, Martell, José María, and Pérez, Carlos. "Extensions of Rubio de Francia's extrapolation theorem.." Collectanea Mathematica 57.Extra (2006): 195-231. <http://eudml.org/doc/41785>.

@article{Cruz2006,
abstract = {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.},
author = {Cruz-Uribe, David, Martell, José María, Pérez, Carlos},
journal = {Collectanea Mathematica},
keywords = {Análisis de Fourier; Integrales singulares; Operadores maximales; Extrapolación; extrapolation of weighted norm inequalities; weights; rearrangement invariant function spaces; modular inequalities; maximal functions; singular integrals; commutators; fractional integrals},
language = {eng},
number = {Extra},
pages = {195-231},
title = {Extensions of Rubio de Francia's extrapolation theorem.},
url = {http://eudml.org/doc/41785},
volume = {57},
year = {2006},
}

TY - JOUR
AU - Cruz-Uribe, David
AU - Martell, José María
AU - Pérez, Carlos
TI - Extensions of Rubio de Francia's extrapolation theorem.
JO - Collectanea Mathematica
PY - 2006
VL - 57
IS - Extra
SP - 195
EP - 231
AB - 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.
LA - eng
KW - Análisis de Fourier; Integrales singulares; Operadores maximales; Extrapolación; extrapolation of weighted norm inequalities; weights; rearrangement invariant function spaces; modular inequalities; maximal functions; singular integrals; commutators; fractional integrals
UR - http://eudml.org/doc/41785
ER -