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Revisiting Riesz transforms on Heisenberg groups (1110.3236v1)
Published 14 Oct 2011 in math.FA
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.
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