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 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 note we prove that the ball is a maximiser for integer order Schatten p-norms of the
Riesz potential operators among all domains of a given measure in R d. In particular, the …

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 the dependence of the best constants in Sobolev and Gagliardo–Nirenberg
inequalities on the precise form of the Sobolev space norm is investigated. The analysis is …

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 …

We propose analogues of Green's and Picone's identities for the p-sub-Laplacian on
stratified Lie groups. In particular, these imply a generalised Díaz-Saá inequality. Using …

This book is an attempt to collect a number of properties emerging in recent research
describing certain features of the theory of partial differential equations that can be attributed …

In this paper we prove that the circular cylinder is a maximizer of the Schatten p-norm of
generalized heat potential operators among all Euclidean cylindric domains of a given …

We construct Green functions of Dirichlet boundary value problems for sub-Laplacians on
certain unbounded domains of a prototype Heisenberg-type group (prototype H-type group …