Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series
R. Gundy, R. Wheeden (1974)
Studia Mathematica
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R. Gundy, R. Wheeden (1974)
Studia Mathematica
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Angel Gatto, Cristian Gutiérrez (1983)
Studia Mathematica
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Y. Rakotondratsimba (1994)
Publicacions Matemàtiques
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For some pairs of weight functions u, v which satisfy the well-known Muckenhoupt conditions, we derive the boundedness of the maximal fractional operator M (0 ≤ s < n) from L to L with q < p.
R. Coifman, C. Fefferman (1974)
Studia Mathematica
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Michael Christ (1984)
Studia Mathematica
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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.
Kenneth Andersen, Russel John (1981)
Studia Mathematica
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Shuichi Sato (1989)
Studia Mathematica
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E. Sawyer (1985)
Studia Mathematica
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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 < ∞.