Revista Matemática Iberoamericana


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Volume 28, Issue 4, 2012, pp. 1091–1108
DOI: 10.4171/RMI/704

Published online: 2012-10-14

Revisiting Riesz transforms on Heisenberg groups

P. K. Sanjay[1] and Sundaram Thangavelu[2]

(1) Indian Institute of Science, Bangalore, India
(2) Indian Institute of Science, Bangalore, India

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.

Keywords: Riesz transforms, Heisenberg groups, Fourier multipliers, Hermite functions, Laguerre functions

Sanjay P. K., Thangavelu Sundaram: Revisiting Riesz transforms on Heisenberg groups. Rev. Mat. Iberoamericana 28 (2012), 1091-1108. doi: 10.4171/RMI/704