Embeddings between weighted Copson and Cesàro function spaces

Гогатишвили, Амиран; Mustafayev, Rza; Ünver, Tuğçe

doi:10.21136/cmj.2017.0424-16

Cited by 9 publications

(13 citation statements)

References 30 publications

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“…Remark 2. Note that, when p = q or r = 1, this problem is not interesting since it reduces to the characterizations of Hardy-type inequalities and can be found in [9], therefore we will consider the cases when r < 1. On the other hand, we have the restriction p < q, which arises from the duality argument.…”

Section: Resultsmentioning

confidence: 99%

“…There is more than one motivation to study inclusion between Cesàro and Copson spaces. First of all when p 1 = q 1 or p 2 = q 2 , weighted Cesàro and Copson function spaces coincide with some weighted Lebesgue spaces (see [9,), thus inequality (1) is a generalization of the well-known weighted direct and reverse Hardy-type inequalities (e.g. [15,7,19]).…”

Section: Introductionmentioning

confidence: 99%

“…w(t)t q , t > 0, under the restriction q 1 in order to characterize the embeddings between some Lorentz-type spaces. Recently, in [9] the two sided estimates for the best constant in (1) is given for four weights and four parameters 0 < p 1 ; p 2 ; q 1 ; q 2 < 1 under the restriction p 2 q 2 . Moreover, using these results, in [9, Theorems 3.11-3.12], the associate spaces of weighted Copson and Cesàro function spaces were characterized and in [10] pointwise multipliers between Cesàro and Copson function spaces are given for some ranges of parameters.…”

Section: Introductionmentioning

confidence: 99%

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Embeddings between weighted Tandori and Cesàro function spaces

Yildiz¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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We characterize the weights for which the two-operator inequalityholds for all non-negative measurable functions on (0; 1), where 0 < p < q 1 and 0 < r < 1, namely, we …nd the least constants in the embeddings between weighted Tandori and Cesàro function spaces. We use the combination of duality arguments for weighted Lebesgue spaces and weighted Tandori spaces with weighted estimates for the iterated integral operators.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Embeddings between weighted Tandori and Cesàro function spaces

Yildiz¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…For example, duality techniques reduce the embeddings between Lorentz-type spaces, Morrey-type spaces and Cesáro-type spaces to the weighted iterated inequalities (see, e.g. [3,5,7,27]).…”

Section: Letmentioning

confidence: 99%

Weighted inequalities involving iteration of two Hardy integral operators

Гогатишвили¹,

Ünver²

2022

Preprint

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f (x)dx, for all non-negative measurable functions on (a, b), −∞ ≤ a < b ≤ ∞. We construct a more straightforward discretization method than those previously presented in the literature, and we characterize this inequality in both discrete and continuous forms.2010 Mathematics Subject Classification. 26D10. Key words and phrases. weighted Hardy inequality, iterated operators, Copson operator, Hardy operator, inequalities for monotone functions. Recently,in [4], with a new and simpler discretization technique requires neither parameter restrictions nor non-degeneracy conditions, characterization of (1.1) is given. We adapt this approach to the specific demands of the inequality considered in this paper.

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“…[8, Lemma 3.13] Let β be a positive number. Suppose that g, h ∈ M + (0, ∞) and a ∈ W(0, ∞) is non-decreasing.…”

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confidence: 99%