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 …

" The book describes how functional inequalities are often manifestations of natural
mathematical structures and physical phenomena, and how a few general principles …

For a general subcritical second-order elliptic operator P in a domain Ω⊂ R n (or
noncompact manifold), we construct Hardy-weight W which is optimal in the following sense …

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 continue our previous study of improved Hardy, Rellich and uncertainty principle
inequalities on a Riemannian manifold $ M $, started in our earlier paper from 2009. In the …

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 …

Factorizations and Hardy and Hardy–Rellich inequalities Page 1 J. Spectr. Theory 10 (2020),
1277–1302 DOI 10.4171/JST/327 Journal of Spectral Theory © European Mathematical …

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 …

Let M be a complete, simply connected Riemannian manifold with negative curvature. We
obtain the sharp constants of Hardy and Rellich inequalities related to the geodesic distance …

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 …