Weighted inequalities for a class of semiadditive operators

Oinarov, Ryskul; Kalybay, Aigerim

doi:10.15352/afa/06-4-155

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Cited by 12 publications

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“…That work is a natural extension of the theory of weighted strong-type iterated Hardy inequalities that has been developed in last years (see [3,[8][9][10][11]16,17,19]).…”

Section: Introduction and Resultsmentioning

confidence: 99%

Weighted weak-type iterated Hardy–Copson inequalities

García,

Salvador

2024

Anal Math

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“…That work is a natural extension of the theory of weighted strong-type iterated Hardy inequalities that has been developed in last years (see [3,[8][9][10][11]16,17,19]).…”

Section: Introduction and Resultsmentioning

confidence: 99%

Weighted weak-type iterated Hardy–Copson inequalities

García,

Salvador

2024

Anal Math

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“…The result was later revisited several times, see e.g. [3,27], where also further applications to bilinear operators are pointed out. Inequalities for superposition of the Copson and Hardy operators were studied in [15]; however, the results obtained there were restricted to nondegenerate weights.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

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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“…The main aim of this paper is to find necessary and sufficient conditions on the weights , V, and for the validity of inequalities (1) and (2) in the case 1 < , , < ∞. The same problem for (⋅, ⋅) = 1 was considered in [9,10].…”

Section: Introductionmentioning

confidence: 99%