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 but requires the detailed analysis of the wave equation on these groups due to Müller and Seeger. We highlight and develop the connection between sharp bounds for oscillating multipliers and the problem of determining the minimal amount of smoothness required for Mihlin-Hörmander multipliers, a problem that was solved for groups of Heisenberg type but remains open for other groups.
Oscillating spectral multipliers on groups of Heisenberg type
Paolo Ciatti
Membro del Collaboration Group
;
2022
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 but requires the detailed analysis of the wave equation on these groups due to Müller and Seeger. We highlight and develop the connection between sharp bounds for oscillating multipliers and the problem of determining the minimal amount of smoothness required for Mihlin-Hörmander multipliers, a problem that was solved for groups of Heisenberg type but remains open for other groups.File in questo prodotto:
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