Maximal functions related to subelliptic operators with polynomially growing coefficients (Q1894819)

Let \(N\) be a simply connected nilpotent Lie group. On \(N \times \mathbb{R}^ +\) certain \(N\)-invariant second order subelliptic operators \(L\) are considered. Let \(\mu'\) be the corresponding family of harmonic measures on \(N \times \mathbb{R}^ +\). Under some assumptions on \(L\) the maximal functions \[ M_ 0 f(x) = \sup_{0 < t < 1} | f * \mu^ t (x) |,\quad M_ \infty f(x) = \sup_{t \geq 1} | f* \mu^ t (x)| \] are of weak type (1,1).