• In the Heisenberg group of dimension 2 n+ 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 Lp 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. © 2021, The Author(s).

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Heisenberg group

Littlewood–Paley–Stein operators

Riesz transforms

Sub-Laplacian with drift

Heisenberg group

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