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Artículo
Sharp weighted estimates for approximating dyadic operators
(American Mathematical Society, 2010)
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 ...
Artículo
Extrapolation from A∞ weights and applications
(Elsevier, 2004-08-15)
We generalize the Ap extrapolation theorem of Rubio de Francia to A∞ weights in the context of Muckenhoupt bases. Our result has several important features. First, it can be used to prove weak endpoint inequalities starting ...
Capítulo de Libro
A note on the off-diagonal Muckenhoupt-Wheeden conjecture
(World Scientific, 2016)
We obtain the off-diagonal Muckenhoupt-Wheeden conjec-ture for Calder´on-Zygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the Hardy-Littlewood maximal functionsatisfies the following two weight ...
Artículo
Sharp weighted estimates for classical operators
(Elsevier, 2012-01-15)
We prove sharp one and two-weight norm inequalities for some of the classical operators of harmonic analysis: the Hilbert and Riesz transforms, the Beurling-Ahlfors operator, the maximal singular integrals associated to ...
Artículo
Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators
(Indiana University, 2000)
We give Ap-type conditions which are sufficient for the two-weight, weak-type (p, p) inequalities for fractional integral operators, Calderón-Zygmund operators and commutators. For fractional integral operators, this solves ...
Artículo
Artículo
Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture
(Elsevier, 2007-12-20)
We prove two-weight norm inequalities for Calderón-Zygmund singular integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for ...
Artículo
Two weight extrapolation via the maximal operator
(Elsevier, 2000-06-20)
We give several extrapolation theorems for pairs of weights of the form (w, Mkw) and (w, (Mw/w)r w), where w is any non-negative function, r>1, and Mk is the kth iterate of the Hardy–Littlewood maximal operator. As an ...
Artículo
Extensions of Rubio de Francia's extrapolation theorem
(Universitat de Barcelona, 2006)
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, ...
Artículo
Two-weight, weak-type norm inequalities for singular integral operators
(International Press, 1999)
We give a sufficient condition for singular integral operators and, more generally, Calder´on-Zygmund operators to satisfy the weak (p, p) inequality u({x ∈ R n : |T f(x)| > t}) ≤ C / tp Z Rn |f|p v dx, 1 < p < ∞. Our ...