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 …

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–
Kohn–Nirenberg type inequalities on stratified groups and study some of their …

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 …

Hardy type inequalities have been also studied intensively on homogeneous Carnot groups.
These problems are important in the analysis of sub-Laplacian and p-sub-Laplacian on …

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 …

We prove L p-Caffarelli–Kohn–Nirenberg type inequalities on homogeneous groups, which
is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also …

We establish sharp remainder terms of the L 2-Caffarelli–Kohn–Nirenberg inequalities on
homogeneous groups, yielding the inequalities with best constants. Our methods also give …

We analyze local (central) Morrey spaces, generalized local (central) Morrey spaces and
Campanato spaces on homogeneous groups. The boundedness of the Hardy-Littlewood …

We prove a range of critical Hardy inequalities and uncertainty type principles on one of
most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups …