Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups

Journal article, 2022

In the Heisenberg group of dimension 2n+1, we consider the sub-Laplacian with a drift in the horizontal coordinates. There is a related measure for which this operator is symmetric. The corresponding Riesz transforms are known to be L^p bounded with respect to this measure.
We prove that the Riesz transforms of order 1 are also of weak type (1,1), and that this is false for order 3 and above. Further, we consider the related
maximal Littlewood-Paley-Stein operators and prove the weak type (1,1) for those of order 1 and disprove it for higher orders.