Fourier multipliers on the Heisenberg group revisited

Article Type

Research Article

Publication Title

Studia Mathematica

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.

First Page

241

Last Page

272

DOI

10.4064/sm190413-14-10

Publication Date

1-1-2021

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