The purpose of this monograph is to give an exposition of the global quantization of
operators on nilpotent homogeneous Lie groups. We also present the background analysis …

In this paper, we develop the global symbolic calculus of pseudo-differential operators
generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) …

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 …

We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic
differential operators. More precisely, given vector fields $ X_1,\ldots, X_m $ on a smooth …

Let G be a unimodular type I second countable locally compact group and let ̂G be its
unitary dual. We introduce and study a global pseudo-differential calculus for operator …

In this paper we study the Cauchy problem for the wave equations for hypoelliptic
homogeneous left-invariant operators on graded Lie groups when the time-dependent non …

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 article, we investigate spectral properties of the sublaplacian G on the Engel group,
which is the main example of a Carnot group of step 3. We develop a new approach to 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 …

In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We
particularise to this group our general construction [4],[2],[3] of pseudo-differential calculi on …