4 papers
Unweighted Hardy Inequalities on the Heisenberg Group and in Step-Two Carnot Groups
Lorenzo d'Arca, Luca Fanelli, Valentina Franceschi +1
We establish unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layer, with explicit lower bounds for the optimal Hardy constant. The approa…
A unified approach to Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings
Lorenzo D'Arca
We present a unified and concise method for establishing L^p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a…
A unified approach to Hardy-type inequalities with Bessel pairs
Lucrezia Cossetti, Lorenzo D'Arca
In this paper, we provide suitable characterisations of pairs of weights known as Bessel pairs, that ensure the validity of weighted Hardy-type inequalities. The abstract…
Weighted Poincaré inequality and Hardy improvements related to some degenerate elliptic differential operators
Lorenzo D'Arca
In this paper, we characterize the sharp constant and maximizing functions for weighted Poincaré inequalities. These results lead to refinements of Hardy's inequality obtained by…