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Browsing by Author "Pérez Moreno, Carlos"
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Maximal functions and the control of weighted inequalities for the fractional integral operator [Article]
Carro Rosell, María Jesús; Pérez Moreno, Carlos; Soria de Diego, Fernando; Soria de Diego, Francisco Javier (Indiana University, 2005)We study weaktype (1, 1) weighted inequalities for the fractional integral operator Iα. We show that the fractional maximal operator Mα controls these inequalities when the weight is radially decreasing. However, we exhibit ...

Minimal regularity conditions for the endpoint estimate of bilinear CalderónZygmund operators [Article]
Pérez Moreno, Carlos; Torres, Rodolfo H. (American Mathematical Society, 20140109)Minimal regularity conditions on the kernels of bilinear operators are identi fied and shown to be sufficient for the existence of endpoint estimates within the context of the bilinear CalderónZygmund theory.

Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer [Article]
Ombrosi, Sheldy J.; Pérez Moreno, Carlos (Uniwersytetu i Politechniki, 2016)In this paper we study mixed weighted weaktype inequalities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from D. CruzUribe, ...

New estimates for the maximal singular integral [Article]
Mateu Bennassar, Joan Eugeni; Orobitg Huguet, Joan; Pérez Moreno, Carlos; Verdera Melenchón, Joan (Oxford University Press, 2010)In this paper we pursue the study of the problem of controlling the maximal singular integral T∗ f by the singular integral T f. Here T is a smooth homogeneous Calder´onZygmund singular integral of convolution type. ...

New maximal functions and multiple weights for the multilinear CalderónZygmund theory [Article]
Lerner, Andrei K.; Ombrosi, Sheldy J.; Pérez Moreno, Carlos; Torres, Rodolfo H.; Trujillo González, Rodrigo Francisco (Elsevier, 20090301)A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the mfold product of the HardyLittlewood maximal function is studied. The operator is used to obtain a precise control ...

On sufficient conditions for the boundedness of the HardyLittlewood maximal operator between weighted Lpspaces with different weights [Article]
Pérez Moreno, Carlos (London Mathematical Society, 199507) 
Optimal exponents in weighted estimates without examples [Article]
Luque Martínez, Teresa; Pérez Moreno, Carlos; Rela, Ezequiel (International Press, 2015)t. We present a general approach for proving the optimality of the exponents on weighted estimates. We show that if an operator T satisfies a bound like kT kLp(w) ≤ c [w] β Ap w ∈ Ap, then the optimal lower bound ...

Potential operators, maximal functions, and generalizations of A∞ [Article]
Pérez Moreno, Carlos; Wheeden, Richard L. (Springer, 200308)We derive weighted norm estimates which relate integral operators of potential type (fractional integrals) to corresponding maximal operators (fractional maximal operators). We also derive norm estimates for the maximal ...

El principio de CalderónZygmund [Chapter of Book]
Pérez Moreno, Carlos; Trujillo González, Rodrigo Francisco (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 ...

Quantitative weighted mixed weaktype inequalities for classical operators [Article]
Ombrosi, Sheldy J.; Pérez Moreno, Carlos; Recchi, Diana Jorgelina (Indiana University, 2016)We improve on several mixed weaktype inequalities both for the HardyLittlewood maximal function and for CalderónZygmund operators. These types of inequalities were considered by Muckenhoupt and Wheeden and later on by ...

Reverse Hölder property for strong weights and general measures [Article]
Luque Martínez, Teresa; Pérez Moreno, Carlos; Rela, Ezequiel (Springer, 20160222)We present dimensionfree reverse H¨older inequalities for strong A∗p weights, 1 ≤ p < ∞. We also provide a proof for the full range of local integrability of A∗1 weights. The common ingredient is a multidimensional version ...

Sharp bounds for general commutators on weighted Lebesgue spaces [Article]
Chung, Daewon; Pereyra, María Cristina; Pérez Moreno, Carlos (American Mathematical Society, 2012)We show that if a linear operator T is bounded on weighted Lebesgue space L2(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a ...

Sharp estimates for commutators of singular integrals via iterations of the HardyLittlewood maximal function [Article]
Pérez Moreno, Carlos (Springer, 199711) 
Sharp Lpweighted Sobolev inequalities [Article]
Pérez Moreno, Carlos (Association des Annales de l'Institut Fourier, 1995) 
Sharp reverse Hölder property for A∞ weights on spaces of homogeneous type [Article]
Hytönen, Tuomas; Pérez Moreno, Carlos; Rela, Ezequiel (Elsevier, 20121215)In this article we present a new proof of a sharp Reverse Hölder Inequality for A∞ weights. Then we derive two applications: a precise open property of Muckenhoupt classes and, as a consequence of this last result, we ...

Sharp twoweight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture [Article]
Cruz Uribe, David; Martell Berrocal, José María; Pérez Moreno, Carlos (Elsevier, 20071220)We prove twoweight norm inequalities for CalderónZygmund 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 ...

Sharp weighted bounds for fractional integral operators [Article]
Lacey, Michael T.; Moen, Kabe; Pérez Moreno, Carlos; Torres, Rodolfo H. (Elsevier, 20100901)The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral ...

Sharp weighted bounds for multilinear maximal functions and CalderónZygmund operators [Article]
Damián González, Wendolín; Lerner, Andrei K.; Pérez Moreno, Carlos (Springer, 201502)In this paper we prove some sharp weighted norm inequalities for the multi(sub)linear maximal function M introduced in [18] A.K. Lerner, S. Ombrosi, C. Pérez, R.H. Torres and R. TrujilloGonz´alez, New maximal functions ...

Sharp weighted bounds involving A∞ [Article]
Hytönen, Tuomas; Pérez Moreno, Carlos (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 ...

Sharp weighted endpoint estimates for commutators of singular integral operators [Article]
Pérez Moreno, Carlos; Pradolini, Gladis (University of Michigan, 2001)