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 transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.
Cite this article
P. K. Sanjay, Sundaram Thangavelu, Revisiting Riesz transforms on Heisenberg groups. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1091–1108DOI 10.4171/RMI/704