David Cruz-Uribe, Carlos Pérez (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We give type conditions which are sufficient for two-weight, strong inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function . Our results extend earlier work on weak inequalities in [13].
Robert Sharpley, Yong-Sun Shim (1989)
Studia Mathematica
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Javier Duoandikoetxea (1991)
Publicacions Matemàtiques
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The aim of this paper is to review a set of articles ([6], [10], [11], [13], [16], [25]) of which José Luis Rubio de Francia was author and co-author written between 1985 and 1987.
A. Cordoba, C. Fefferman (1976)
Studia Mathematica
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Irina Asekritova, Natan Krugljak, Lech Maligranda, Lars-Erik Persson (1997)
Studia Mathematica
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There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition....
Alberto Criado, Fernando Soria (2016)
Studia Mathematica
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In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical...
Robert Fefferman (1986)
Revista Matemática Iberoamericana
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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].
Richard L. Wheeden (1993)
Publicacions Matemàtiques
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Sufficient conditions are derived in order that there exist strong-type weighted norm inequalities for some off-centered maximal functions. The maximal functions are of Hardy-Littlewood and fractional types taken over starlike sets in R. The sufficient conditions are close to necessary and extend some previously known weak-type results.
Robert Fefferman (1985)
Revista Matemática Iberoamericana
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A. Cianchi, R. Kerman, B. Opic, L. Pick (2000)
Studia Mathematica
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We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
Y. Rakotondratsimba (1998)
Collectanea Mathematica
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It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.