Related papers: Hardy inequalities with homogenuous weights
In this paper, we got several sharp Hardy-Littlewood-Sobolev-type inequalities on quaternionic Heisenberg groups (a general form due to Folland and Stein [FS74]), using the symmetrization-free method in a paper of Frank and Lieb [FL12],…
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the…
In this article we study some new pointwise inequalities between rough singular integral operators, weighted maximal functions of the gradient and weighted Morrey spaces. These pointwise estimates will naturally lead us to a new class of…
Let $\Omega$ be a bounded domain of $\mathbb{R}^N$ whose boundary is a $\mathbb{C}^2$ compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights…
Let $(X,\mathbf{q},\mu)$ be an ultra-RD-space with upper dimension $n\in(0,\infty)$; i.e., it is a quasi-ultrametric space of homogeneous type whose measure $\mu$ satisfies an additional reverse doubling property. Let…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
We state a version of Gehring's self improvement Theorem for reverse \Holder weights which is valid for dyadic cubes over spaces of homogeneous type and explore some of the consequences and applications.
We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space $\ell^p$ with $p\in(0,1]$, we develop characterizations which enable us to reduce the problem to…
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…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a usual compact space $\mathcal M$, Gr\"ochenig introduced the weighted least squares polynomials and the least squares quadrature from pointwise samples of a function, and…
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 state and discuss several interrelated results, conjectures, and questions regarding contractive inequalities for classical $H^p$ spaces of the unit disc. We study both coefficient estimates in terms of weighted $\ell^2$ sums and the…
We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singularities. We also investigate the existence of critical points and…
This paper is concerned with derivation of the global or local in time Strichartz estimates for radially symmetric solutions of the free wave equation from some Morawetz-type estimates via weighted Hardy-Littlewood-Sobolev (HLS)…
We study the blow-up behaviour of minimizing sequences for the singular Moser-Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can…
Let $1\leq p <\infty$ and $0 < q,r < \infty$. We characterize the validity of the inequality for the composition of the Hardy operator, \begin{equation*} \bigg(\int_a^b \bigg(\int_a^x \bigg(\int_a^t f(s)ds \bigg)^q u(t) dt…
In this paper we prove sharp Hardy inequalities by using Maximal function theory. Our results improve and extend the well-known results of G.Hardy \cite{Ha04}, T.Cazenave \cite {Ca03}, J.-Y.Chemin\cite {Ch06} and T.Tao\cite {TT06}.
In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under…