Related papers: Dynamic Hardy type inequalities via alpha-conforma…
In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
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. Our arguments build on certain weighted inequalities based on…
When studying the weighted Hardy-Rellich inequality in $L^2$ with the full gradient replaced by the radial derivative the best constant becomes trivially larger or equal than in the first situation. Our contribution is to determine the new…
In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance.…
We establish fractional Hardy inequality on bounded domains in $\mathbb{R}^{d}$ with inverse of distance function from smooth boundary of codimension $k$, where $k=2, \dots,d$, as weight function. The case $sp=k$ is the critical case, where…
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
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 derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
We present an approach to the factorization method for second order difference equations on time scales. We construct Hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order…
The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla derivatives; (ii) to extend previous results by using the more…
We prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical Hardy…
In this article we use the Bellman function technique to characterize the measures for which the weighted Hardy's inequality holds on dyadic trees. We enunciate the (dual) Hardy's inequality over the dyadic tree and we use the associated…
By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an…
In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and…
We prove that in variable exponent spaces $L^{p(\cdot)}(\Omega)$, where $p(\cdot)$ satisfies the log-condition and $\Omega$ is a bounded domain in $\mathbf R^n$ with the property that $\mathbf R^n \backslash \bar{\Omega}$ has the cone…
We consider weighted $L^p$-Hardy inequalities involving the distance to the boundary of a domain in the $n$-dimensional Euclidean space with nonempty boundary. Using criticality theory, we give an alternative proof of the following result…