تحويلات ريس على زمر هايزنبرغ

Abstract

In this paper, we characterize higher order Riesz transforms on the Heisenberg group and show that they satisfy dimension_ free bounds under some assumptions on the multipliers. We introduce the reduced Heisenberg group, and we show that dimension_ free estimates for Riesz transforms on H^n, which depends very much on the dilation structure of H^n, does not work for the reduced Heisenberg group. However, we can view the Riesz transforms on the Heisenberg group (reduced Heisenberg group) as an operator valued multiplier for the Fourier transform.