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Fourier multipliers on the Heisenberg group revisited

Volume 260 / 2021

Sayan Bagchi 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.

Authors

  • Sayan BagchiStat-Math Unit
    Indian Statistical Institute
    Kolkata, India
    Current address:
    Department of Mathematics and Statistics
    Indian Institute of Science Education and Research Kolkata
    Mohanpur 741246, Nadia, West Bengal, India
    e-mail

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