Revisiting Riesz transforms on Heisenberg groups

Abstract

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transfer- ence theorems, we deduce boundedness theorems for Riesz trans- forms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre ex- pansions.

19 pages. To appear in Revista Math. Ibero

Cited by in corpus (2)

• Dimension free boundedness of Riesz transforms for the Grushin operator
• Riesz transforms and multipliers for the Grushin operator