This open access book provides an extensive treatment of Hardy inequalities and closely
related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The …

A complete Riemannian manifold equipped with some potential function and an invariant
conformal measure is referred to as a complete smooth metric measure space. This paper …

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 …

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 …

We study Hardy-type inequalities associated to the quadratic form of the shifted Laplacian−
Δ HN−(N− 1) 2/4 on the hyperbolic space HN,(N− 1) 2/4 being, as it is well-known, the …

We establish sharpened forms of the Hardy type identities and inequalities which are
substantial improvements of Hardy inequalities for the operators− Δ H−(N− 1) 2 4 on the …

In this paper, we prove several new Hardy type inequalities (such as the weighted Hardy
inequality, weighted Rellich inequality, critical Hardy inequality and critical Rellich …

We prove optimal improvements of the Hardy inequality on the hyperbolic space. Here,
optimal means that the resulting operator is critical in the sense of Devyver, Fraas, and …

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 …

We prove a family of Hardy–Rellich and Poincaré identities and inequalities on the
hyperbolic space having, as particular cases, improved Hardy-Rellich, Rellich and second …