Weighted Hardy’s inequalities for negative indices

Prokhorov, D. V.

doi:10.5565/publmat_48204_08

Cited by 14 publications

(11 citation statements)

References 5 publications

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“…Proposition 2.16 supplements the results of the Prokhorov recent paper [11], and Proposition 2.17 supplements the results of the papers [12], [13].…”

Section: Y)dλ(y)supporting

confidence: 69%

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Persson

Степанов

Ushakova

2006

Proc. Amer. Math. Soc.

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“…Proposition 2.16 supplements the results of the Prokhorov recent paper [11], and Proposition 2.17 supplements the results of the papers [12], [13].…”

Section: Y)dλ(y)supporting

confidence: 69%

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Persson

Степанов

Ushakova

2006

Proc. Amer. Math. Soc.

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“…D.V. Prokhorov in [53] gave the precise characterization of (0.7) for the same range of parameters p, q, as Beesack and Heinig. He also established a duality between the cases p, q < 0 and 0 < p, q < 1.…”

Section: Introductionmentioning

confidence: 94%

“…Theorem 2 [53]. Let −∞ < p, q < 0, 0 < C < +∞, k be a non-negative measurable function on (a, b) × (a, b) and…”

Section: Introductionmentioning

confidence: 99%

Hardy-type inequalities on the cones of monotone functions

Popova

2012

Sib Math J

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This Licentiate thesis deals with Hardy-type inequalities restricted to cones of monotone functions. The thesis consists of two papers (paper A and paper B) and an introduction which gives an overview to this specific field of functional analysis and also serves to put the papers into a more general frame. We deal with positive σ-finite Borel measures on R + := [0, ∞) and the class M ↓ (M ↑) consisting of all non-increasing (non-decreasing) Borel functions f : R + → [0, +∞]. In paper A some two-sided inequalities for Hardy operators on the cones of monotone functions are proved. The idea to study such equivalences follows from the Hardy inequality

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“…(см., например, монографии [10], [15], [52], [56], [64], статьи [3], [4], [118], [16]- [18], [57]- [60], [70], [71], [80]- [86], [92]- [109], [113] и др. ).…”

Section: интегральные операторыunclassified

Редукционные Теоремы Для Весовых Интегральных Неравенств На Конусе Монотонных Функций

Гогатишвили¹,

Степанов²

2013

Uspekhi Mat. Nauk

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Редукционные теоремы для весовых интегральных неравенств на конусе монотонных функций А. Гогатишвили, В. Д. Степанов В работе дается обзор результатов, связанных с редукцией интеграль-ных неравенств с положительными операторами в весовых пространствах Лебега на вещественной полуоси на конусе монотонных функций к некото-рым неравенствам на конусе неотрицательных функций, для доказатель-ства которых имеется больше возможностей. При этом случай монотон-ных операторов является новым. В качестве приложения для ряда опе-раторов Вольтерра получена полная характеризация при всех возможных параметрах суммирования.Библиография: 118 названий.Ключевые слова: весовое пространство Лебега, конус монотонных функций, весовое интегральное неравенство, принцип двойственности, ограниченные операторы, редукционная теорема.

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Weighted Hardy’s inequalities for negative indices

Abstract: In the paper we obtain a precise characterization of Hardy type inequalities with weights for the negative indices and the indices between 0 and 1 and establish a duality between these cases.

Cited by 14 publications

References 5 publications

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions

Hardy-type inequalities on the cones of monotone functions

Редукционные Теоремы Для Весовых Интегральных Неравенств На Конусе Монотонных Функций

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