A convolution type characterization for Lp - multipliers for the Heisenberg group

It is well known that if m is an Lp - multiplier for the Fourier transform on ℝn(1<p<∞) , then there exists a pseudomeasure σ such that Tmf  =σ*f. A similar result is proved for the group Fourier transform on the Heisenberg group Hn. Though this result is already known in generality for amenable groups, a simple proof is provided in this paper