3 papers
math.AP2026
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…
math.AP2025
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…
math.AP2024
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 a…