Related papers: Hardy inequalities for weighted Dirac operatos
In this paper, we study the asymptotic behaviour of the sharp constant in discrete Hardy and Rellich inequality on the lattice $\mathbb{Z}^d$ as $d \rightarrow \infty$. In the process, we proved some Hardy-type inequalities for the…
The paper is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in…
We deal with weighted Hardy-Sobolev type inequalities for functions on $\mathbb{R}^d$, $d\geq 2$. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…
In this paper, we establish a general weighted Hardy type inequality for the $% p-$Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present…
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 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…
Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the…
New proofs of the classical Hermite-Hadamard inequality are presented and several applications are given, including Hadamard-type inequalities for the functions, whose derivatives have inflection points or whose derivatives are convex.…
Applying methods of Real Analysis and Functional Analysis, we build two weight functions with parameters and provide two kinds of parameterized Yang-Hilbert-type integral inequalities with the best constant factors. Equivalent forms, the…
We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. We prove that the superharmonicity of the weight function provides a sufficient condition to obtain Hardy inequalities.…
We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…
We study the following finite-rank Hardy-Lieb-Thirring inequality of Hardy-Schr\"odinger operator: \begin{equation*} \sum_{i=1}^N\left|\lambda_i\Big(-\Delta-\frac{c}{|x|^2}-V\Big)\right|^s\leq C_{s,d}^{(N)}\int_{\mathbb R^d}V_+^{s+\frac…
We study the two-weighted estimate \[ \bigg\|\sum_{k=0}^na_k(x)\int_0^xt^kf(t)dt|L_{q,v}(0,\infty)\bigg\|\leq c\|f|L_{p,u}(0,\infty)\|,\tag{$*$} \] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<p\leq…
We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich inequalities to hold, and propose a new way to use the notion of Bessel pair to establish the optimal Hardy-Rellich type inequalities. Our results…
Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
In this paper, we investigate further the weighted $p(x)$-Hardy inequality with the additional term of the form \[ \int_\Omega |\xi|^{p(x)}\mu_{1,\beta} (dx) \leqslant \int_\Omega |\nabla \xi|^{p(x)}\mu_{2,\beta} (dx)+\int_\Omega…
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}…