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 show that the classical Hardy inequalities with optimal constants in the Sobolev spaces
$ W_0^{1, p} $ and in higher-order Sobolev spaces on a bounded domain $\Omega\subset …

Hardy-type inequalities related to degenerate elliptic differential operators Page 1 Ann. Scuola
Norm. Sup. Pisa Cl. Sci. (5) Vol. IV (2005), 451-486 Hardy-type inequalities related to …

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 prove a simple sufficient criterion to obtain some Hardy inequalities on Riemannian
manifolds related to quasilinear second order differential operator Δ pu:= div (|∇ u| p− 2∇ …

We prove Hardy inequalities for the conformally invariant fractional powers of the
sublaplacian on the Heisenberg group H n. We prove two versions of such inequalities …

Hardy Inequalities Related to Grushin Type Operators Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 132, Number 3, Pages 725-734 S 0002-9939(03)07232-0 …

Here, the existence of at least one positive radial solution of the Nonlinear
nonhomogeneous Neumann problem− Δ H nu+ R (ξ) u= a (| ξ| H n)| u| q− 2 u 1+| u| q− p− b …

The existence of at least one positive radial solution of the p-biharmonic problem Δ H n (w
(ξ)| Δ H nu| p− 2 Δ H nu)+ R (ξ) w (ξ)| u| p− 2 u=∑ i= 1 mai (| ξ| H n)| u| qi− 2 u−∑ j= 1 kbj (| ξ …