Weighted inequalities for the two-dimensional Hardy operator
E. Sawyer (1985)
Studia Mathematica
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E. Sawyer (1985)
Studia Mathematica
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Chen, Tieling (2003)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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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.
Amiran Gogatishvili, Canay Aykol, Vagif S. Guliyev (2015)
Studia Mathematica
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We characterize associate spaces of generalized weighted weak-Lorentz spaces and use this characterization to study embeddings between these spaces.
Ana Lucía Bernardis, Francisco Javier Martín-Reyes (2002)
Publicacions Matemàtiques
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Let φ: R → [0,∞) an integrable function such that φχ = 0 and φ is decreasing in (0,∞). Let τf(x) = f(x-h), with h ∈ R {0} and f(x) = 1/R f(x/R), with R > 0. In this paper we characterize the pair of weights (u, v) such that the operators Mf(x) = sup|f| * [τφ](x) are of weak type (p, p) with respect to (u, v), 1 < p < ∞.
Kenneth Andersen, Benjamin Muckenhoupt (1982)
Studia 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.
R. Kerman, A. Torchinsky (1982)
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. ...
Qinsheng Lai (1995)
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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Alois Kufner, Lars-Erik Persson, Anna Wedestig (2004)
Banach Center Publications
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James Adedayo Oguntuase (2001)
Kragujevac Journal of Mathematics
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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.