Results 1 to 10 of about 1,396,305 (234)

On the best possible remaining term in the Hardy inequality [PDF]

Proceedings of the National Academy of Sciences of the United States of America, 2008
We give a necessary and sufficient condition on a radially symmetric potential V on a bounded domain Ω of ℝn that makes it an admissible candidate for an improved Hardy inequality of the following type.
Nassif Ghoussoub
exaly   +4 more sources

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
doaj   +2 more sources

Fractional boundary Hardy inequality for the critical cases [PDF]

Journal of Functional Analysis, 2023
We establish generalised fractional boundary Hardy-type inequality, in the spirit of Caffarelli-Kohn-Nirenberg inequality for different values of $s$ and $p$ on various domains in $\mathbb{R}^d, ~ d \geq 1$.
Adimurthi, Prosenjit Roy, Vivek Sahu
semanticscholar   +1 more source

Optimal Hardy Inequality for Fractional Laplacians on the Integers [PDF]

Annales de l'Institute Henri Poincare. Physique theorique, 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 constant.
M. Keller, Marius Nietschmann
semanticscholar   +1 more source

An Improved One-Dimensional Hardy Inequality [PDF]

Journal of Mathematical Sciences, 2022
. We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our motivation comes
R. Frank, A. Laptev, T. Weidl
semanticscholar   +1 more source

Improvement of the Discrete Hardy inequality [PDF]

Bulletin des Sciences Mathématiques, 2022
We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl.
Prasun Roychowdhury, D. Suragan
semanticscholar   +1 more source

A Sharp Form of the Discrete Hardy Inequality and the Keller–Pinchover–Pogorzelski Inequality [PDF]

The American mathematical monthly, 2021
We give a short proof of a recently established Hardy-type inequality due to Keller, Pinchover, and Pogorzelski together with its optimality. Moreover, we identify the remainder term which makes it into an identity.
D. Krejčiřík, F. Štampach
semanticscholar   +1 more source

Discrete Weighted Hardy Inequality in 1-D [PDF]

Journal of Mathematical Analysis and Applications, 2021
. In this paper we consider weighted versions of one dimensional discrete Hardy’s inequality on the half-line with power weights of the form n α ; namely, we consider: We prove the above inequality when α ∈ [0 , 1) ∪ [5 , ∞ ) with the sharp constant c ...
S. Gupta
semanticscholar   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source