Displaying similar documents to “A quantitative approach to weighted Carleson condition”

A weighted version of Journé's lemma.

Donald Krug, Alberto Torchinsky (1994)

Revista Matemática Iberoamericana

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In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces H (R x R ) and a description of their duals when p is close to 1.

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.

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...

Solvability of the Poisson equation in weighted Sobolev spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.

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...

Existence of solutions to the Poisson equation in L₂-weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

Sharp one-weight and two-weight bounds for maximal operators

Kabe Moen (2009)

Studia Mathematica

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We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm...