Dazhao Chen (2014)
Colloquium Mathematicae
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We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.
Dashan Fan, Shuichi Sato (2004)
Studia Mathematica
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We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
Liliana De Rosa, Carlos Segovia (1990)
Colloquium Mathematicae
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Kenneth Andersen, Russel John (1981)
Studia Mathematica
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R. Coifman, C. Fefferman (1974)
Studia Mathematica
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María Lorente, María Silvina Riveros (2002)
Commentationes Mathematicae Universitatis Carolinae
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We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in ) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1),...
Vakhtang Kokilashvili, Alexander Meskhi (2014)
Banach Center Publications
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We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.
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 < ∞.
Angel Gatto, Cristian Gutiérrez (1983)
Studia Mathematica
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A. Lerner (2000)
Studia Mathematica
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We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, and BLO-norm inequalities
Sokhadze, Z. (2000)
Memoirs on Differential Equations and Mathematical Physics
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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.