Related papers: Hardy's theorem for compact Lie groups

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.

In the setting of spaces of homogeneous type, we study some Hardy type inequalities, which notably appeared in the proofs of local T(b) theorems as in [AR]. We give some suffi cient conditions ensuring their validity, related to the…

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

The Hardy-Littlewood inequality on $\mathbb{T}$ compares the $L^p$-norm of a function with a weighted $\ell^p$-norm of its Fourier coefficients. The approach has recently been studied for compact homogeneous spaces and we study a natural…

In this paper, we obtain a fractional Hardy inequality in the case $Q<sp$ on homogeneous Lie groups, and as an application we show the corresponding uncertainty principle. Also, we show a fractional Hardy-Sobolev type inequality on…

We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we obtain some…

We prove an exact analogue of Ingham's uncertainty principle for the group Fourier transform on the Heisenberg group. This is accomplished by explicitly constructing compactly supported functions on the Heisenberg group whose…

A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…

We investigate locally compact topological groups for which a generalized analogue of Heisenberg uncertainty inequality hold. In particular, it is shown that this inequality holds for $\mathbb{R}^n \times K$ (where $K$ is a separable…

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category 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…

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.

We prove various Hardy-type and uncertainty inequalities on a stratified Lie group $G$. In particular, we show that the operators $T_\alpha: f \mapsto |.|^{-\alpha} L^{-\alpha/2} f$, where $|.|$ is a homogeneous norm, $0 < \alpha < Q/p$,…

We prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical Hardy…

We continue our previous study of improved Hardy, Rellich and Uncertainty principle inequalities on a Riemannian manifold $M$, started in \cite{Kombe-Ozaydin}. In the present paper we prove new weighted Hardy-Poincar\'e, Rellich type…

The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…

We establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood-Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.

We prove an equivalence result between the validity of a pointwise Hardy inequality in a domain and uniform capacity density of the complement. This result is new even in Euclidean spaces, but our methods apply in general metric spaces as…

We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…

We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions…