Revisiting Riesz transforms on Heisenberg groups
  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. 
P.K.Sanjay and S.Thangavelu
math.FA