Characterizations of reverse dynamic weighted Hardy-type inequalities with kernels on time scales

S. H. Saker; M. M. Osman; D. O’Regan; R. P. Agarwal

doi:10.1007/s00010-020-00759-6

Characterizations of reverse dynamic weighted Hardy-type inequalities with kernels on time scales

S. H. Saker, M. M. Osman, D. O’Regan, R. P. Agarwal

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we establish some conditions on nonnegative rd-continuous weight functions u(x) and υ(x) which ensure that a reverse dynamic inequality of the form (∫a∞fp(x)υ(x)Δx)1p≤C(∫a∞u(x)(∫aσ(x)K(σ(x),σ(y))f(y)Δy)qΔx)1q,holds when q≤ p< 0 and 0 < q≤ p< 1. Corresponding dual results are also obtained. In particular, we prove some reverse dynamic weighted Hardy-type inequalities with kernels on time scales which as special cases contain some generalizations of integral and discrete inequalities due to Beesack and Heinig.

Original language	English
Pages (from-to)	125-146
Number of pages	22
Journal	Aequationes Mathematicae
Volume	95
Issue number	1
DOIs	https://doi.org/10.1007/s00010-020-00759-6
Publication status	Published - Feb 2021

Keywords

Dynamic inequalities
Reversed Hardy’s inequality
Time scales

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Saker, SH;Osman, MM;O'Regan, D;Agarwal, RP

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10.1007/s00010-020-00759-6

Cite this

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abstract = "In this paper, we establish some conditions on nonnegative rd-continuous weight functions u(x) and υ(x) which ensure that a reverse dynamic inequality of the form (∫a∞fp(x)υ(x)Δx)1p≤C(∫a∞u(x)(∫aσ(x)K(σ(x),σ(y))f(y)Δy)qΔx)1q,holds when q≤ p< 0 and 0 < q≤ p< 1. Corresponding dual results are also obtained. In particular, we prove some reverse dynamic weighted Hardy-type inequalities with kernels on time scales which as special cases contain some generalizations of integral and discrete inequalities due to Beesack and Heinig.",

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AU - O’Regan, D.

AU - Agarwal, R. P.

PY - 2021/2

Y1 - 2021/2

N2 - In this paper, we establish some conditions on nonnegative rd-continuous weight functions u(x) and υ(x) which ensure that a reverse dynamic inequality of the form (∫a∞fp(x)υ(x)Δx)1p≤C(∫a∞u(x)(∫aσ(x)K(σ(x),σ(y))f(y)Δy)qΔx)1q,holds when q≤ p< 0 and 0 < q≤ p< 1. Corresponding dual results are also obtained. In particular, we prove some reverse dynamic weighted Hardy-type inequalities with kernels on time scales which as special cases contain some generalizations of integral and discrete inequalities due to Beesack and Heinig.

AB - In this paper, we establish some conditions on nonnegative rd-continuous weight functions u(x) and υ(x) which ensure that a reverse dynamic inequality of the form (∫a∞fp(x)υ(x)Δx)1p≤C(∫a∞u(x)(∫aσ(x)K(σ(x),σ(y))f(y)Δy)qΔx)1q,holds when q≤ p< 0 and 0 < q≤ p< 1. Corresponding dual results are also obtained. In particular, we prove some reverse dynamic weighted Hardy-type inequalities with kernels on time scales which as special cases contain some generalizations of integral and discrete inequalities due to Beesack and Heinig.

KW - Dynamic inequalities

KW - Reversed Hardy’s inequality

KW - Time scales

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DO - 10.1007/s00010-020-00759-6

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Characterizations of reverse dynamic weighted Hardy-type inequalities with kernels on time scales

Abstract

Keywords

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