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Czechoslovak Mathematical Journal, 2014 Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{α-1} \int_0^x t^{-α} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved.
Maligranda, Lech +2 more
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On a higher-order Hardy inequality [PDF]
, 1999 summary:The Hardy inequality $\int_\Omega|u(x)|^pd(x)^{-p}\dd x\le c\int_\Omega|\nabla u(x)|^p\dd x$ with $d(x)=\operatorname{dist}(x,\partial\Omega)$ holds for $u\in C^\infty_0(\Omega)$ if $\Omega\subset\Bbb R^n$ is an open set with a sufficiently ...
Edmunds, David E., Rákosník, Jiří
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q-Hardy type inequalities for quantum integrals
Advances in Difference Equations, 2021 The aim of this work is to obtain quantum estimates for q-Hardy type integral inequalities on quantum calculus. For this, we establish new identities including quantum derivatives and quantum numbers.
Necmettin Alp, Mehmet Zeki Sarikaya
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Optimal Hardy Inequality for Fractional Laplacians on the Integers
, 2022 We study the fractional Hardy inequality on the integers. We prove the optimality of the Hardy weight and hence affirmatively answer the question of sharpness of the ...
Nietschmann, Marius, Keller, Matthias
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Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities
Journal of Function Spaces and Applications, 2009 We prove a new general one-dimensional inequality for convex functions and Hardy–Littlewood averages. Furthermore, we apply this result to unify and refine the so-called Boas's inequality and the strengthened inequalities of the Hardy–Knopp–type ...
Aleksandra Čižmešija +2 more
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A note on Hardy’s inequality [PDF]
Journal of Inequalities and Applications, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chu, Yu-Ming, Xu, Qian, Zhang, Xiao-Ming
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On the improvement of the Hardy inequality due to singular magnetic fields [PDF]
, 2020 We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes into account ...
Vega L. +11 more
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A Reverse Hardy-Hilbert’s Inequality Involving One Partial Sum as the Terms of Double Series
Journal of Function Spaces, 2022 In this paper, by constructing proper weight coefficients and utilizing the Euler-Maclaurin summation formula and the Abel partial summation formula, we establish reverse Hardy-Hilbert’s inequality involving one partial sum as the terms of double series.
Bicheng Yang, Shanhe Wu, Xingshou Huang
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On an Inequality of H. G. Hardy [PDF]
Journal of Inequalities and Applications, 2010 We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918.
Sajid Iqbal +2 more
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An Equality Underlying Hardy’s Inequality [PDF]
The American Mathematical Monthly, 2022 A classical inequality of G. H. Hardy states that Cx≤2x for x in l2, where C is the Cesàro (alias averaging) operator. This inequality has been strengthened to (C−I)x≤x. It has also been shown that CTx≤Cx for x in l2. We present equalities that imply these inequalities, together with the reverse inequalities (C−I)x≥(1/√2)x and Cx≤√2CTx. We also present
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