A convolution type characterization for L-P-multipliers for the Heisenberg group

It is well known that if m is an L-P-multiplier for the Fourier transform on R-n (1 < p < infinity), then there exists a pseudomeasure sigma such that T(m)f = sigma * f. A similar result is proved for the group Fourier transform on the Heisenberg group H-n. Though this result is already known in generality for amenable groups, a simple proof is provided in this paper.