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 …

In this work we establish sharp kernel conditions ensuring that the corresponding integral
operators belong to Schatten-von Neumann classes. The conditions are given in terms of …

In this paper we extend classical Titchmarsh theorems on the Fourier transform of Hölder–
Lipschitz functions to the setting of compact homogeneous manifolds. As an application, we …

We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and
study their spectral properties. We prove that these operators have a pure point spectrum …

On semilinear equations with free boundary conditions on stratified Lie groups - ScienceDirect
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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 …