Eugenio Hernández (1991)
Publicacions Matemàtiques
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In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined...
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.
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.
E. Sawyer (1985)
Studia Mathematica
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Elida Ferreyra (1990)
Studia Mathematica
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Suixin He, Shuangping Tao (2023)
Czechoslovak Mathematical Journal
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We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators.
C.J. NEUGEBAUER (1992)
Forum mathematicum
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Pedro Ortega Salvador (2000)
Collectanea Mathematica
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Suket Kumar (2018)
Commentationes Mathematicae Universitatis Carolinae
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Hardy inequalities for the Hardy-type operators are characterized in the amalgam space which involves Banach function space and sequence space.
Appel, Matthew J., Bourdon, Paul S., Thrall, John J. (1996)
Experimental Mathematics
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Allen L. Shields (1983)
Mathematische Zeitschrift
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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...
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.