Extrapolation on the cone of decreasing functions

Carro, María Jesús Casals; Marcoci, Anca N.; Marcoci, Liviu G.

doi:10.1016/j.jat.2012.02.005

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…convergence of the partial spherical Fourier integrals or in the solvability of the Dirichlet problem for the Laplacian on planar domains. See [12][13][14] and references therein for more information on such operators. Another possible application is related to traces of Sobolev functions.…”

Section: Introductionmentioning

confidence: 99%

Optimal behavior of weighted Hardy operators on rearrangement‐invariant spaces

Mihula

2023

Mathematische Nachrichten

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The behavior of certain weighted Hardy‐type operators on rearrangement‐invariant function spaces is thoroughly studied. Emphasis is put on the optimality of the obtained results. First, the optimal rearrangement‐invariant function spaces guaranteeing the boundedness of the operators from/to a given rearrangement‐invariant function space are described. Second, the optimal rearrangement‐invariant function norms being sometimes complicated, the question of whether and how they can be simplified to more manageable expressions is addressed. Next, the relation between optimal rearrangement‐invariant function spaces and interpolation spaces is investigated. Last, iterated weighted Hardy‐type operators are also studied.

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Section: Introductionmentioning

confidence: 99%

Optimal behavior of weighted Hardy operators on rearrangement‐invariant spaces

Mihula

2023

Mathematische Nachrichten

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“…For example, thanks to our results, we get under control the optimal behavior of upper bounds, which are even sharp in some cases, for nonincreasing rearrangements of not only various less-standard (nonfractional and fractional) maximal operators ( [29,41]) but also operators with certain behavior of their operator norms, which play a role in the a.e. convergence of the partial spherical Fourier integrals or in the solvability of the Dirichlet problem for the Laplacian on planar domains ( [12,11,14] and references therein). Another possible application is related to traces of Sobolev functions.…”

Section: Introductionmentioning

confidence: 99%

Optimal behavior of weighted Hardy operators on rearrangement-invariant spaces

Mihula¹

2021

Preprint

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The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function spaces-that is, the best possible function spaces within the class of rearrangement-invariant function spaces-guaranteeing the boundedness of the operators from/to a given rearrangement-invariant function space are described. Second, the optimal rearrangement-invariant function norms being sometimes complicated, the question of whether and how they can be simplified to more manageable expressions, arguably more useful in practice, is addressed. Last, iterated weighted Hardy-type operators are also studied.Besides aiming to provide a comprehensive treatment of the optimal behavior of the operators on rearrangement-invariant function spaces in one place, the paper is motivated by its applicability in various fields of mathematical analysis, such as harmonic analysis, extrapolation theory or the theory of Sobolev-type spaces.

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Exact Calculation of Sums of Cones in Lorentz Spaces

Бережной

2018

Funct Anal Its Appl

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Extrapolation on the cone of decreasing functions

Cited by 4 publications

References 16 publications

Optimal behavior of weighted Hardy operators on rearrangement‐invariant spaces

Optimal behavior of weighted Hardy operators on rearrangement‐invariant spaces

Optimal behavior of weighted Hardy operators on rearrangement-invariant spaces

Exact Calculation of Sums of Cones in Lorentz Spaces

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