Results 31 to 40 of about 1,396,305 (234)

Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

Bulletin of Mathematical Sciences, 2020
In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: ∫ℍ ...
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan   +2 more
doaj   +1 more source

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
doaj   +1 more source

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, Sabir Hussain, Josip Pečarić   +2 more
doaj   +1 more source

Remarks on the hardy inequality

Journal of Inequalities and Applications, 1997
Let be an open subset of with finite Lebesgue -measure, let be the distance from to the boundary of , and let . We give a simple direct proof that if satisfies the plumpness condition of Martio and Väisälä [10], then the inequality ...
Hurri–Syrjänen R, Edmunds DE
doaj   +2 more sources

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
doaj   +1 more source

Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

, 2017
We propose the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups and prove continuity results for them.
Michael Ruzhansky, D. Suragan
semanticscholar   +1 more source

The Hardy inequality and the heat equation with magnetic field in any dimension [PDF]

, 2014
In the Euclidean space of any dimension d, we consider the heat semigroup generated by the magnetic Schrödinger operator from which an inverse-square potential is subtracted to make the operator critical in the magnetic-free case.
C. Cazacu, D. Krejčiřík
semanticscholar   +1 more source

Characterizations for fractional Hardy inequality [PDF]

, 2013
We provide a Maz'ya-type characterization for a fractional Hardy inequality. As an application, we show that a bounded open set G admits a fractional Hardy inequality if and only if the associated fractional capacity is quasiadditive with respect to ...
Bartłomiej Dyda, A. Vähäkangas
semanticscholar   +1 more source

On a Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

Mathematics
In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to ...
Bicheng Yang, Shanhe Wu
doaj   +1 more source

On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain

Advances in Nonlinear Analysis, 2021
We study the wave inequality with a Hardy ...
Jleli Mohamed, Samet Bessem, Vetro Calogero   +2 more
doaj   +1 more source