Related papers: A generalization of Hilbert's inequality
We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.
We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…
We give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_{0}^{\infty}f^{p}v\right)^{\frac{1}{p}}. \end{equation*} The…
In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider…
There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of…
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 improve the classical discrete Hardy inequality for $ 1<p<\infty $ for functions on the natural numbers. For integer values of $ p $ the Hardy weight is an absolutely monotonic function.
A version of the Cauchy-Schwarz inequality in operator theory is the following: for any two symmetric, positive definite matrices $A,B \in \mathbb{R}^{n \times n}$ and arbitrary $X \in \mathbb{R}^{n \times n}$ $$ \|AXB\| \leq \|A^2…
We obtain a series improvement to higher-order $L^p$-Rellich inequalities on a Riemannian manifold $M$. The improvement is shown to be sharp as each new term of the series is added.
An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight $r^{-b}$ for functions in $\R^n$. The exact Hardy constant $c_b=c_b(n)$ is found and generalized minimizers are given. The constant $c_b$…
In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that…
We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization
In this paper we prove Holder regularity of the gradient for solutions of Dirichlet problem associate to degenerate elliptic equations, extending the recent result of Imbert and Silvestre. Indeed we obtain regularity up to the boundary and…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
The Hardy Inequality (HI) for potentials with countably many singularities of the form $V=\sum_{k\in \mathbf{Z}}\frac{1}{|x-a_k|^2}$ is not a trivial issue. In principle, the more singular poles are, the less the Hardy constant is: it is…
We study the $P_1$ finite element approximation of the best constant in the classical Hardy inequality over bounded domains containing the origin in $\mathbb{R}^N$, for $N \geq 3$. Despite the fact that this constant is not attained in the…
Young's convolution inequality provides an upper bound for the convolution of functions in terms of $L^p$ norms. It is known that for certain groups, including Heisenberg groups, the optimal constant in this inequality is equal to that for…
The Hardy--Littlewood inequalities for $m$-linear forms on $\ell_{p}$ spaces are known just for $p>m$. The critical case $p=m$ was overlooked for obvious technical reasons and, up to now, the only known estimate is the trivial one. In this…
In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, H\"older-Rogers,…
In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].