Weighted bilinear Hardy inequalities

Cañestro, M. Isabel Aguilar; Salvador, P.; Torreblanca, Consuelo Ramírez

doi:10.1016/j.jmaa.2011.08.078

Cited by 35 publications

(19 citation statements)

References 10 publications

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“…with constant c independent of f and g, where T i = H or H * , i = 1, 2, are equivalent to inequalities (1.5)-(1.6) and (1.7)-(1.8) (see, for instance, [1]). It is well-known that when T is a integral operator then by substitution of variables it is possible to change the cone of non-decreasing functions to the cone of non-increasing functions and vice versa, when considering inequalities…”

Section: Hg(t)mentioning

confidence: 99%

On weighted iterated Hardy-type inequalities

Гогатишвили

Mustafayev

2017

Positivity

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Abstract. In this paper a reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in weighted Lebesgue spaces are proved. New equivalence theorems are obtained for the operator T to be bounded in weighted Lebesgue spaces restricted to the cones of monotone functions, which allow to change the cone of non-decreasing functions to the cone of non-increasing functions and vice versa not changing the operator T . New characterizations of the weighted Hardy-type inequalities on the cones of monotone functions are given. The validity of so-called weighted iterated Hardy-type inequalities are characterized.

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Section: Hg(t)mentioning

confidence: 99%

On weighted iterated Hardy-type inequalities

Гогатишвили

Mustafayev

2017

Positivity

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“…The paper [1] motivated the work presented here. Indeed, here we consider a restricted version of (4) which may be called the bilinear Hardy inequality for nonincreasing functions and written in the form…”

mentioning

confidence: 91%

“…The covered range of exponents in there was 1 < p, q < ∞. For some related results see also the references in [1].…”

mentioning

confidence: 98%

See 2 more Smart Citations

Bilinear weighted Hardy inequality for nonincreasing functions

Křepela

2017

Publicacions Matemàtiques

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New characterization of weighted inequalities involving superposition of Hardy integral operators

Gogatishvili,

Ünver

2024

Mathematische Nachrichten

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Let and . We characterize the validity of the inequality for the composition of the Hardy operator, for all non‐negative measurable functions on , . We construct a more straightforward discretization method than those previously presented in the literature, and we provide some new scales of weight characterizations of this inequality in both discrete and continuous forms and we obtain previous characterizations as the special case of the parameter.

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Weighted bilinear Hardy inequalities

Cited by 35 publications

References 10 publications

On weighted iterated Hardy-type inequalities

On weighted iterated Hardy-type inequalities

Bilinear weighted Hardy inequality for nonincreasing functions

New characterization of weighted inequalities involving superposition of Hardy integral operators

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