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Displaying similar documents to “Rearrangement estimates of the area integrals”

A remark on Fefferman-Stein's inequalities.

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.

Estimates for the arctangent function related to Shafer's inequality

Cristinel Mortici, H. M. Srivastava (2014)

Colloquium Mathematicae

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The aim of this article is to give new refinements and sharpenings of Shafer's inequality involving the arctangent function. These are obtained by means of a change of variables, which makes the computations much easier than the classical approach.

Weighted Estimates for the Maximal Operator of a Multilinear Singular Integral

Xi Chen (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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An improved multiple Cotlar inequality is obtained. From this result, weighted norm inequalities for the maximal operator of a multilinear singular integral including weak and strong estimates are deduced under the multiple weights constructed recently.

Two weighted inequalities for convolution maximal operators.

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 < ∞.

Muckenhoupt-Wheeden conjectures in higher dimensions

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...

A semi-discrete Littlewood-Paley inequality

J. M. Wilson (2002)

Studia Mathematica

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We apply a decomposition lemma of Uchiyama and results of the author to obtain good weighted Littlewood-Paley estimates for linear sums of functions satisfying reasonable decay, smoothness, and cancellation conditions. The heart of our application is a combinatorial trick treating m-fold dilates of dyadic cubes. We use our estimates to obtain new weighted inequalities for Bergman-type spaces defined on upper half-spaces in one and two parameters, extending earlier work of R. L. Wheeden...