JournalsrmiOnline First2 August 2021

Oscillating spectral multipliers on groups of Heisenberg type

  • Roberto Bramati

    Politecnico di Torino, Italy
  • Paolo Ciatti

    Università degli Studi di Padova, Italy
  • John Green

    University of Edinburgh, UK
  • James Wright

    University of Edinburgh, UK
Oscillating spectral multipliers on groups of Heisenberg type cover
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Abstract

We establish endpoint estimates for a class of oscillating spectral multipliers on Lie groups of Heisenberg type. The analysis follows an earlier argument due to the second and fourth author [Springer INdAM Ser., vol. 45 (2021)], but requires the detailed analysis of the wave equation on these groups due to Müller and Seeger [Anal. PDE 8 (2015)].

We highlight and develop the connection between sharp bounds for oscillating spectral multipliers and the problem of determining the minimal amount of smoothness required for Mihlin–Hörmander multipliers, a problem that has been solved for groups of Heisenberg type but remains open for other groups.

Cite this article

Roberto Bramati, Paolo Ciatti, John Green, James Wright, Oscillating spectral multipliers on groups of Heisenberg type. Rev. Mat. Iberoam. (2021), published online first

DOI 10.4171/RMI/1302