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One-dimensional differential Hardy inequality [PDF]

Journal of Inequalities and Applications, 2017
We establish necessary and sufficient conditions for the one-dimensional differential Hardy inequality to hold, including the overdetermined case. The solution is given in terms different from those of the known results.
Aigerim Kalybay
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Finsler Hardy–Kato's inequality [PDF]

Journal of Mathematical Analysis and Applications, 2019
We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by \cite{AFV} in Euclidean context. Also we discuss the validity of the same type of inequalities on open cones.
Alvino, A., Ferone, A., Mercaldo, A., Takahashi, F., Volpicelli, R.   +4 more
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A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums

Mathematics, 2021
In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers ...
Bicheng Yang, Shanhe Wu, Xingshou Huang
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A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series

Journal of Mathematics, 2021
In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series.
Jianquan Liao, Shanhe Wu, Bicheng Yang
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Some new scales of characterization of Hardy’s inequality; pp. 7–18 [PDF]

Proceedings of the Estonian Academy of Sciences, 2010
Let 1 lt; p ≤ q lt; ∞. Inspired by some recent results concerning Hardy-type inequalities where the equivalence of four scales of integral conditions was proved, we use related ideas to find ten new equivalence scales of integral conditions.
Amiran Gogatishvili, Alois Kufner, Lars-Erik Persson   +2 more
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Remarks on Some Higher Dimensional Hardy Inequalities

International Journal of Analysis and Applications, 2023
In this note, we give an elementary proof of Hardy inequality in higher dimensions introduced by Christ and Grafakos. The advantage of our approach is that it uses the one-dimensional Hardy inequality to obtain higher dimensional versions.
Zraiqat Amjad, Jebril Iqbal, Hawawsheh Laith, Abudayah Mohmammad   +3 more
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A Weighted Generalization of Hardy–Hilbert-Type Inequality Involving Two Partial Sums

Mathematics, 2023
In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial summation formula, and differential mean value theorem, a new
Bicheng Yang, Shanhe Wu
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A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum

Mathematics, 2022
In this work, by introducing multiple parameters and utilizing the Euler–Maclaurin summation formula and Abel’s partial summation formula, we first establish a reverse Hardy–Hilbert’s inequality containing one partial sum as the terms of double series ...
Bicheng Yang, Shanhe Wu, Xingshou Huang
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Hardy inequalities [PDF]

Proceedings of the American Mathematical Society, 1990
Here the following Hardy inequalities are studied \[ ∑ k = 0 m − 1 ∫ | ∇
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Hardy-type inequalities

Journal of the European Mathematical Society, 2004
In this well-written paper, the authors study operators of the form $L=-\\Delta -µd^{-2}$, where $d(x)={\\rm dist}(x,\\Sigma)$, $µ\\in R$ and $\\Sigma \\subset R^{n}$. More precisely, they study inequalities which suggest that the operator $L$ has a positive first eigenvalue.
Davila, Juan, Dupaigne, Louis
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