Title: Fourier Multipliers on the Heisenberg groups revisited,
Abstract: In this paper, we give explicit expressions of differential-difference
operators appeared in the hypothesis of the general Fourier multiplier theorem
associated to the Heisenberg groups proved by Mauceri and De Micheal for one
dimension and C. Lin for higher dimension. We also give a much shorter proof of
the above-mentioned theorem. Then we obtain a sharp weighted estimate for
Fourier multipliers on the Heisenberg groups.