ω-Calderón-Zygmund operators
Sijue Wu (1995)
Studia Mathematica
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We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when .
Sijue Wu (1995)
Studia Mathematica
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We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when .
Joan Cerdà, Joaquim Martín (2000)
Studia Mathematica
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Many problems in analysis are described as weighted norm inequalities that have given rise to different classes of weights, such as -weights of Muckenhoupt and -weights of Ariño and Muckenhoupt. Our purpose is to show that different classes of weights are related by means of composition with classical transforms. A typical example is the family of weights w for which the Hardy transform is -bounded. A -weight is precisely one for which its Hardy transform is in , and also a weight...
Vakhtang Kokilashvili, Alexander Meskhi (2006)
Banach Center Publications
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Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.
Canqin Tang, Feien Xue, Yu Zhou (2011)
Annales Polonici Mathematici
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A sufficient condition for boundedness on Herz-type spaces of the commutator generated by a Lipschitz function and a weighted Hardy operator is obtained.
Ze-Hua Zhou, Yu-Xia Liang, Xing-Tang Dong (2012)
Annales Polonici Mathematici
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This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
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...
Raman Adegoke, James Adedayo Oguntuase (2001)
Kragujevac Journal of Mathematics
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E. Sawyer (1985)
Studia Mathematica
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Steven Bloom, Ron Kerman (1994)
Studia Mathematica
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Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for to hold when and are N-functions with convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.
Steven Bloom (1990)
Studia Mathematica
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Josefina Alvarez, Richard Bagby, Douglas Kurtz, Carlos Pérez (1993)
Studia Mathematica
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We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
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].
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.
Steven Bloom (1997)
Studia Mathematica
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Let , where k is a nonnegative kernel increasing in x, decreasing in y, and satisfying a triangle inequality. An nth-order Opial inequality has the form . Such inequalities can always be simplified to nth-order reduced inequalities, where the exponent . When n = 1, the reduced inequality is a standard weighted norm inequality, and characterizing the weights is easy. We also find necessary and sufficient conditions on the weights for second-order reduced Opial inequalities to hold. ...
Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2013)
Annales de l’institut Fourier
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A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov–Clark measures which corresponds to the unweighted case, that is, to the...
Alois Kufner, Lars-Erik Persson, Anna Wedestig (2004)
Banach Center Publications
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