Lorenzo D'Arca

Unweighted Hardy inequalities on the Heisenberg group and in step-two Carnot groups

Lorenzo D'Arca, Luca Fanelli, Valentina Franceschi, Dario Prandi

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 approach is based on a quantitative integration-by-parts mechanism that replaces the non-horizontal Euler vector field by a suitably constructed …

Unweighted Hardy Inequalities on the Heisenberg Group and in Step-Two Carnot Groups

Lorenzo D'Arca, Luca Fanelli, Valentina Franceschi, Dario Prandi

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 approach is based on a quantitative integration-by-parts mechanism that replaces the non-horizontal Euler vector field by a suitably constructed …

it, es, fr (code pays fourni par la source)

Functional inequalities of hardy-rellich type in euclidean and non-euclidean settings

Lorenzo D'Arca

In this PhD thesis we study functional inequalities associated with degenerate elliptic and subelliptic operators, with a particular focus on Hardy, Rellich, and Hardy-Rellich inequalities. Our analysis covers both Euclidean and non-Euclidean settings, including operators such as the Kohn Laplacian on the …

A unified approach to $L^{p}$ Hardy and Rellich-type inequalities in Euclidean and non-Euclidean settings

Lorenzo D'Arca

Abstract We present a unified and concise method for establishing $L^{p}$ L p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on maximizing sequences and …

it (code pays fourni par la source)

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 $(V,W),$ known as Bessel pairs, that ensure the validity of weighted Hardy-type inequalities. The abstract approach adopted here makes it possible to establish such inequalities also going beyond the classical Euclidean …

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 adding remainder terms involving \(L^p\) norms. We use techniques that avoid symmetric rearrangement argument, simplifying the analysis …