On the higher Riesz transforms for the Heisenberg group

Using the definition of the higher Riesz transforms for Heisenberg group, together with the spectral decomposition of functions belong to L2 spaces and the properties of the special Hermite functions, we obtain the convolution kernels for these transforms. Moreover, we show that those kernels satisfy the Calderon-Zygmund singular conditions, then one can deduce that the Heisenberg higher Riesz transforms are bounded on Lp, 1 p , and are weak type (1,1).