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Article
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 ...
Chapter of Book
El principio de Calderón-Zygmund
(Universidad de La Rioja, 2001)
In this note we show some estimates for multilinear commutators with vector symbol b = (b1,...,bm) defined by the expression Tbf(x) = Z Rn2 4Ym j=1 (bj (x) − bj (y)) 3 5 K(x, y)f(y) dy, where K is the kernel of any ...
Article
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 ...
Article
Sharp weighted estimates for multilinear commutators
(London Mathematical Society, 2002-06)
Multilinear commutators with vector symbol Formula=(b1,…,bm) defined by Formula are considered, where K is a Calderón–Zygmund kernel. The following a priori estimates are proved for w ∈ A∞. For 0 < p < ∞, there exists ...
Article
Borderline weighted estimates for commutators of singular integrals
(Springer, 2016)
In this paper we establish the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cTε2∫RnΦ(∥b∥BMO|f(x)|λ)ML(logL)1+εw(x)dx where w≥0,0<ε<1 and Φ(t)=t(t+log+(t)). This inequality relies upon the following sharp Lp estimate ∥[b ...
Article
Sharp weighted bounds involving A∞
(Mathematical Sciences Publishers, 2013)
We improve on several weighted inequalities of recent interest by replacing a part of the Ap bounds by weaker A∞ estimates involving Wilson’s A∞ constant [w] 0 A∞ := sup Q 1 / w(Q) Z Q M(wχQ). In particular, we show the ...
Article
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, ...