Factorization and extrapolation of pairs of weights
Eugenio Hernández (1989)
Studia Mathematica
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Eugenio Hernández (1989)
Studia Mathematica
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E. Sawyer (1985)
Studia Mathematica
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Pedro Ortega Salvador (2000)
Collectanea Mathematica
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Elida Ferreyra (1990)
Studia Mathematica
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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. ...
Wenjuan Li, Qingying Xue, Kôzô Yabuta (2010)
Studia Mathematica
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Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for...
C.J. NEUGEBAUER (1992)
Forum mathematicum
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Raman Adegoke, James Adedayo Oguntuase (2001)
Kragujevac Journal of Mathematics
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Diening, Lars, Samko, Stefan (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26D10, 46E30, 47B38 We prove the Hardy inequality and a similar inequality for the dual Hardy operator for variable exponent Lebesgue spaces.
Elena Lomakina, Vladimir Stepanov (1998)
Publicacions Matemàtiques
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Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.
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...
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.
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.