Fourier multipliers on the Heisenberg group revisited
Volume 260 / 2021
Studia Mathematica 260 (2021), 241-272
MSC: Primary 43A80, 42B25; Secondary 42B20, 42B35, 33C45.
DOI: 10.4064/sm190413-14-10
Published online: 30 April 2021
Abstract
We give explicit expressions of differential-difference operators that satisfy the hypothesis of the general Fourier multiplier theorem associated to the Heisenberg group proved by Mauceri and De Michele, for one dimension, and Lin, for higher dimensions. We also give a much shorter proof of the above mentioned theorem. Moreover, we obtain a sharp weighted estimate for Fourier multipliers on the Heisenberg group.
