Revisiting Riesz transforms on Heisenberg groups

Details Revisiting Riesz transforms on Heisenberg groups Revisiting Riesz transforms on Heisenberg groups

2011-10-14

arxiv.org/abs/1110.3236v1

Mathematics

Functional Analysis

19 pages. To appear in Revista Math. Ibero

Scientific paper

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.

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