Related papers: A survey of Hardy type inequalities on homogeneous…

In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in…

On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.

In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space on the Heisenberg group with a…

This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group $\mathbb{H}^n$. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and…

We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group $\mathbb{H}^n$. We prove two versions of such inequalities depending on whether the weights involved are non-homogeneous…

In this paper we present $L^2$ and $L^p$ versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the geometric uncertainty principles. We give examples of the…

The aim of this work is to establish some cases of the Caffarelli-Kohn-Nirenberg inequalities on the Heisenberg group for the fractional Sobolev spaces. Here we work with the fractional Sobolev spaces as given by Adimurthi and Mallick in…

We present a unified approach to obtain Hardy-type inequalities in the context of nilpotent Lie groups with sharp constants. The unified methodology employed herein allows for exploration of the sharp Hardy inequalities on various Lie group…

In this paper we discuss cylindrical extensions of improved Hardy, Sobolev type and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants and identities in the spirit of Badiale-Tarantello [2]. All identities are obtained in the…

In this note we formulate recent stability results for Hardy inequalities in the language of Folland and Stein's homogeneous groups. Consequently, we obtain remainder estimates for Rellich type inequalities on homogeneous groups. Main…

In this paper we prove sharp weighted Hardy-type inequalities on Carnot groups with the homogeneous norm $N=u^{1/(2-Q)}$ associated to Folland's fundamental solution $u$ for the sub-Laplacian $\Delta_{\mathbb{G}}$. We also prove uncertainty…

In this paper, we obtain Hardy, Hardy-Rellich and refined Hardy inequalities on general stratified groups and weighted Hardy inequalities on general homogeneous groups using the factorization method of differential operators, inspired by…

In this paper we describe the Euler semigroup $\{e^{-t\mathbb{E}^{*}\mathbb{E}}\}_{t>0}$ on homogeneous Lie groups, which allows us to obtain various types of the Hardy-Sobolev and Gagliardo-Nirenberg type inequalities for the Euler…

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 several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…

In this paper we obtain logarithmic Hardy and Rellich inequalities on general Lie groups. In the case of graded groups, we also show their refinements using the homogeneous Sobolev norms. In fact, we derive a family of weighted logarithmic…

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy…

We give sharp remainder terms of $L^{p}$ and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised…

We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to…

In this paper we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions for an ample class of…