Related papers: Sharp Hardy inequalities in the half space with tr…

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…

We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical…

In the context of Hardy inequalities for the fractional Laplacian $(-\Delta_{\mathbb{N}})^{\sigma}$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_{\sigma}$ for exponents…

We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2, \qquad (a_1,\ldots,a_n) \in \mathbb{R}^n $$ and $$…

We establish sharp Hardy-Adams inequalities on hyperbolic space $\mathbb{B}^{4}$ of dimension four. Namely, we will show that for any $\alpha>0$ there exists a constant $C_{\alpha}>0$ such that \[ \int_{\mathbb{B}^{4}}(e^{32\pi^{2}…

In this paper we obtain an inequality on the unit disc $B$ in the plane, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant $C_0>0$ such that \[…

In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq…

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the…

In this paper we state the weighted Hardy inequality \begin{equation*} c\int_{{\mathbb R}^N}\sum_{i=1}^n \frac{\varphi^2 }{|x-a_i|^2}\, \mu(x)dx\le \int_{{\mathbb R}^N} |\nabla\varphi|^2 \, \mu(x)dx +k \int_{\mathbb{R}^N}\varphi^2 \,…

In this work we establish the following fractional Hardy's inequality $$C\int_{\mathbb{H}^n_+}\frac{|f(\xi)|^p}{x_1^{sp+\alpha}}d\xi\leq \int_{\mathbb{H}^n}\int_{\mathbb{H}^n}\frac{|f(\xi)-f(\xi')|^p}{d({\xi}^{-1}\circ…

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a non-linear and non-local version of the ground state representation.

In this paper, among other results, we improve the best known estimates for the constants of the generalized Bohnenblust-Hille inequality. These enhancements are then used to improve the best known constants of the Hardy--Littlewood…

We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian on the interval with the optimal constant. As a result, we…

In this current work, we revisit the recent improvement of the discrete Hardy's inequality in one dimension and establish an extended improved discrete Hardy's inequality with its optimality. We also study one-dimensional discrete Copson's…

In this paper, we will introduce and study several types of Kakeya inequalities by the maximal functions in Hardy spaces in $\RR^n$,\,$(n\geq2)$, and we could obtain several inequalities associated with the Kakeya inequalities. We will show…

We address the question of attainability of the best constant in the following Hardy-Sobolev inequality on a smooth domain $\Omega$ of \mathbb{R}^n: $$ \mu_s (\Omega) := \inf \{\int_{\Omega}| \nabla u|^2 dx; u \in {H_{1,0}^2(\Omega)}…

In this work we prove sharp $L^p$ versions of multipolar Hardy inequalities in the case of a bipolar potential and $p\geq 2$, which were first developed in the case $p=2$ by Cazacu (CCM 2016) and Cazacu&Zuazua (Studies in phase space…

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 $c_b$…

We consider finite element approximations to the optimal constant for the Hardy inequality with exponent $p=2$ in bounded domains of dimension $n=1$ or $n \geq 3$. For finite element spaces of piecewise linear and continuous functions on a…

We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of…