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 …

We give sharp remainder terms of L p and weighted Hardy and Rellich inequalities on one
of most general subclasses of nilpotent Lie groups, namely the class of homogeneous …

We propose the analogues of boundary layer potentials for the sub-Laplacian on
homogeneous Carnot groups/stratified Lie groups and prove continuity results for them. In …

In this paper we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities: we
show that for $1< p, q<\infty $, $0< r<\infty $ with $ p+ q\geq r $, $\delta\in [0, 1]\cap\left [\frac …

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 …

In this paper we study the Cauchy problem for the semilinear damped wave equation for the
sub-Laplacian on the Heisenberg group. In the case of the positive mass, we show the …

In this paper we derive a variety of functional inequalities for general homogeneous
invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities …

Hardy–Rellich identities with Bessel pairs Page 1 Arch. Math. 113 (2019), 95–112 c 2019
Springer Nature Switzerland AG 0003-889X/19/010095-18 published online April 5, 2019 …

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty
principles for sums of squares of vector fields on bounded sets of smooth manifolds under …

In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on
homogeneous Lie groups. We show analogues of the fractional Sobolev and Hardy …