Oscillating spectral multipliers on groups of Heisenberg type

Roberto Bramati ^[1] ; Paolo Ciatti ^[3] ; John Green ^[2] ; James Wright ^[2]
1. [1] Polytechnic University of Turin
  
  Polytechnic University of Turin
  
  Torino, Italia
2. [2] University of Edinburgh
  
  University of Edinburgh
  
  Reino Unido
3. [3] Dipartimento di Ingegneria Civile, Edile e Ambientale
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Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 5, 2022, págs. 1529-1551
Idioma: inglés
DOI: 10.4171/RMI/1302
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Resumen
- 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