Related papers: Hardy-type Inequalities Via Auxiliary Sequences
We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are…
We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on…
We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
This paper surveys some of our recent progress on Hardy-type inequa\-lities which consist of a well-known topic in Harmonic Analysis. In the first section, we recall the original probabilistic motivation dealing with the stability speed in…
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} 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…
We investigate the existence of closed planar loops with prescribed curvature. Our approach is variational, and relies on a Hardy type inequality and its associated functional space.
We consider a general class of sharp $L^p$ Hardy inequalities in $\R^N$ involving distance from a surface of general codimension $1\leq k\leq N$. We show that we can succesively improve them by adding to the right hand side a lower order…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with…
We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, which converges to the critical Hardy inequality. Sobolev type…
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities…
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces,…
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…
We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal…
General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
We obtain optimal generalized versions of Hardy inequalities, which as special cases contain Hardy's inequality and Hardy's inequality involving the distance function to the boundary of $ \Omega$. In addition we obtain neccesary and…
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…