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Browsing by Author "Pérez Moreno, Carlos"
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A new characterization of the Muckenhoupt Ap weights through an extension of the LorentzShimogaki theorem [Article]
Lerner, Andrei K.; Pérez Moreno, Carlos (Indiana University, 2007)Given any quasiBanach function space X over Rn it is defined an index αX that coincides with the upper Boyd index αX when the space X is rearrangementinvariant. This new index is defined by means of the local maximal ...

A new quantitative two weight theorem for the HardyLittlewood maximal operator [Article]
Pérez Moreno, Carlos; Rela, Ezequiel (American Mathematical Society, 201502)A quantitative two weight theorem for the HardyLittlewood maximal operator is proved improving the known ones. As a consequence a new proof of the main results in [HP] and in [HPR12] is obtained which avoids the use of ...

A note on the offdiagonal MuckenhouptWheeden conjecture [Chapter of Book]
Cruz Uribe, David; Martell Berrocal, José María; Pérez Moreno, Carlos (World Scientific, 2016)We obtain the oﬀdiagonal MuckenhouptWheeden conjecture for Calder´onZygmund operators. Namely, given 1 < p < q < ∞ and a pair of weights (u, v), if the HardyLittlewood maximal functionsatisﬁes the following two weight ...

A pointwise estimate for the kernel of a pseudodifferential operator, with applications [Article]
Álvarez Alonso, Josefina; Hounie, Jorge Guillermo; Pérez Moreno, Carlos (Unión Matemática Argentina, 1991) 
A remark on weighted inequalities for general maximal operators [Article]
Pérez Moreno, Carlos (American Mathematical Society, 199312)Let 1 < p < ∞, and let w, v be two non–negative functions. We give a sufficient condition on w, v for which the general maximal operator MB is bounded from Lp(v) into Lp(w). Our condition is stronger but closely related to ...

A sum operator with applications to selfimproving properties of Poincaré inequalities in metric spaces [Article]
Franchi, Bruno; Pérez Moreno, Carlos; Wheeden, Richard L. (Springer, 200309)We define a class of summation operators with applications to the selfimproving nature of PoincaréSobolev estimates, in fairly general quasimetric spaces of homogeneous type. We show that these sum operators play the ...

A1 bounds for CalderónZygmund operators related to a problem of Muckenhoupt and Wheeden [Article]
Lerner, Andrei K.; Ombrosi, Sheldy J.; Pérez Moreno, Carlos (International Press, 2009)We obtain an Lp(w) bound for CalderónZygmund operators T when w ∈ A1. This bound is sharp both with respect to ∥w∥A1 and with respect to p. As a result, we get a new L1,∞(w) estimate for T related to a problem of Muckenhoupt ...

Ap weights for nondoubling measures in Rn and applications [Article]
Orobitg Huguet, Joan; Pérez Moreno, Carlos (American Mathematical Society, 2002)We study an analogue of the classical theory of Ap(µ) weights in Rn without assuming that the underlying measure µ is doubling. Then, we obtain weighted norm inequalities for the (centered) HardyLittlewood maximal function ...

Borderline weighted estimates for commutators of singular integrals [Article]
Pérez Moreno, Carlos; Rivera Ríos, Israel Pablo (Springer, 2016)In this paper we establish the following estimate w({x∈Rn:[b,T]f(x)>λ})≤cTε2∫RnΦ(∥b∥BMOf(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 ...

Conmutadores de integrales singulares y pesos A1 [PhD Thesis]
Ortiz Caraballo, Carmen María (2011)Esta memoria está estructurada de la siguiente manera: comenzaremos introduciendo en el capítulo 1 las herramientas y definiciones necesarias para entender el desarrollo de las pruebas que se presentan. En el capítulo 2 ...

Endpoint estimates for iterated commutators of multilinear singular integrals [Article]
Pérez Moreno, Carlos; Pradolini, Gladis; Torres, Rodolfo H.; Trujillo González, Rodrigo Francisco (London Mathematical Society, 201402)Iterated commutators of multilinear Calder´onZygmund operators and pointwise multiplication with functions in BMO are studied in products of Lebesgue spaces. Both strong type and weak endpoint estimates are obtained, ...

Endpoint estimates for commutators of singular integral operators [Article]
Pérez Moreno, Carlos (Elsevier, 19950215)We prove endpoint estimates for commutatotrs of singular integrals with BMO functions. We first show that they satisfy L(log L) type inequalities and then that there is a Hardy space type estimate where the usual atomic ...

Estimates with A∞ weights for various singular integral operators [Article]
Alvarez, Josefina; Pérez Moreno, Carlos (Zanichelli, 1994)Si studia la limitazione di certe classi di integrale singolari sullo spazio Lp(w), w € A∞.

Exponential decay estimates for singular integral operators [Article]
Ortiz Caraballo, Carmen María; Pérez Moreno, Carlos; Rela, Ezequiel (Springer, 201312)The following subexponential estimate for commutators is proved {x ∈ Q : [b, T]f(x) > tM2 f(x)} ≤ c e− √ α tkbkBMO Q, t > 0. where c and α are absolute constants, T is a Calder´on–Zygmund operator, M is the Hardy ...

Extensions of Rubio de Francia's extrapolation theorem [Article]
Cruz Uribe, David; Martell Berrocal, José María; Pérez Moreno, Carlos (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, ...

Extrapolation from A∞ weights and applications [Article]
Cruz Uribe, David; Martell Berrocal, José María; Pérez Moreno, Carlos (Elsevier, 20040815)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 ...

Generalized Hörmander conditions and weighted endpoint estimates [Article]
Lorente Domínguez. María; Martell Berrocal, José María; Pérez Moreno, Carlos; Riveros, María Silvina (Polish Academy of Sciences, Institute of Mathematics, 2009)We consider twoweight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove ...

Improving bounds for singular operators via sharp reverse Hölder inequality for A∞ [Chapter of Book]
Ortiz Caraballo, Carmen María; Pérez Moreno, Carlos; Rela, Ezequiel (Springer, 2013)In this expository article we collect and discuss some recent results on different consequences of a Sharp Reverse Hölder Inequality for A∞ weights. For two given operators T and S, we study Lp(w) bounds of CoifmanFefferman ...

L1 → Lq Poincaré inequalities for 0 < q < 1 imply representation formulas [Article]
Lu, Guozhen; Pérez Moreno, Carlos (Springer, 200201)Given two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B0⊂S be a given ball. It has been a wellknown result by now (see [1–4]) that the validity of an L1→L1 Poincaré inequality of the following ...

Lack of natural weighted estimates for some singular integral operators [Article]
Martell Berrocal, José María; Pérez Moreno, Carlos; Trujillo González, Rodrigo Francisco (American Mathematical Society, 2005)