Discretization and antidiscretization of Lorentz norms with no restrictions on weights

Křepela, Martin; Mihula, Zdeněk; Turčinová, Hana

doi:10.1007/s13163-021-00399-7

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…Later various authors spent considerable efforts in order to chip away certain technical obstacles such as nondegeneracy assumptions with varying success -consider e.g. [10] or [23] and the references therein. However, this research is far from being complete.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

“…Indeed, by integrating by parts, it is clear that (23) holds for each k ∈ Z, k < M − 1, whether M = ∞ or M < ∞. The remaining case when M < ∞ and k = M − 1 requires more explanation.…”

Section: We Will First Show Thatmentioning

confidence: 99%

“…On the other hand, since max{A * 4 , B * 2 } < ∞ implies that max{A * 2 , B * 1 } < ∞, by using the same argument we applied in case (ii), ( 23) holds. Then, (8) combined with (23) and (24) yields that…”

Section: We Will First Show Thatmentioning

confidence: 99%

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Weighted inequalities for a superposition of the Copson operator and the Hardy operator

Gogatishvili,

Mihula,

Pick

et al. 2021

Preprint

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in which (a, b) is any nontrivial interval, q, r are positive real parameters and p ∈ (0, 1]. A simple change of variables can be used to obtain any weighted L p -norm with p ≥ 1 on the right-hand side. Another simple change of variables can be used to equivalently turn this inequality into the one in which the Hardy and Copson operators swap their positions. We focus on characterizing those triples of weight functions (u, v, w) for which this inequality holds for all nonnegative measurable functions f with a constant independent of f .We use a new type of approach based on an innovative method of discretization which enables us to avoid duality techniques and therefore to remove various restrictions that appear in earlier work.This paper is dedicated to Professor Stefan Samko on the occasion of his 80th birthday.2010 Mathematics Subject Classification. 26D10.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

Section: We Will First Show Thatmentioning

confidence: 99%

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Weighted inequalities for a superposition of the Copson operator and the Hardy operator

Gogatishvili,

Mihula,

Pick

et al. 2021

Preprint

Self Cite

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“…In correspondence with the appearing of alternative methods, getting rid of various restrictions on parameters is recently becoming possible, see e.g. [38]. Using the characterizations of the inequality (1.1), pointwise multipliers between Cop p 1 ,q 1 (u 1 , v 1 ) and Ces p 2 ,q 2 (u 2 , v 2 ) are given in [22], but again only when p 2 ≤ q 2 .…”

Section: Introductionmentioning

confidence: 99%

Weighted inequalities involving Hardy and Copson operators

Гогатишвили¹,

Pick²,

Ünver³

2022

Preprint

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We characterize a four-weight inequality involving the Hardy operator and the Copson operator. More precisely, given p1, p2, q1, q2 ∈ (0, ∞), we find necessary and sufficient conditions on nonnegative measurable functions u1, u2, v1, v2 on (0, ∞) for which there exists a positive constant c such that the inequalityand classical Lorentz spaces of type Λ.2000 Mathematics Subject Classification. 26D10, 46E20.

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Weighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator

Гогатишвили

Mihula

Pick

et al. 2022

J Fourier Anal Appl

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Discretization and antidiscretization of Lorentz norms with no restrictions on weights

Cited by 4 publications

References 9 publications

Weighted inequalities for a superposition of the Copson operator and the Hardy operator

Weighted inequalities for a superposition of the Copson operator and the Hardy operator

Weighted inequalities involving Hardy and Copson operators

Weighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator

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