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.

Heisenberg group

Littlewood-Paley-Stein operators

sub-Laplacian with drift

Riesz transforms


Hong-Quan Li

Fudan University

Peter Sjögren

Chalmers, Mathematical Sciences

University of Gothenburg

Journal of Fourier Analysis and Applications

1069-5869 (ISSN) 15315851 (eISSN)

Vol. 28 1 10


Basic sciences

Subject Categories

Mathematical Analysis



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