Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
Ewa Damek · Studia Mathematica · 1991
On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e