An -LP Spectral Multiplier Theorem with Sharp p-Specific Regularity Bound on Heisenberg Type Groups

We prove an L p-spectral multiplier theorem for sub-Laplacians on Heisenberg type groups under the sharp regularity condition s > d |1/ p − 1/2|, where d is the topo-logical dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.

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Published in:
Journal of Fourier Analysis and Applications
Publisher:
Springer Science and Business Media LLC
CRC Press
Publishing place:
Cambridge, Mass.
Boca Raton, Fla.
Vol.:
30
No.:
2
ISSN:
1069-5869
ISSN:
1531-5851
Date Issued:
2024
URN:
urn:nbn:de:gbv:8:3-2026-01147-8
DOI:
10.1007/s00041-024-10075-1
Language:
English
Type of Resource:
Text
Publisher:
Springer Science and Business Media LLC
Keywords:
Nilpotent Lie group; Heisenberg type group; Sub-Laplacian; Spectral multiplier; Restriction type estimate; Sub-Riemannian geometry
Classification:
Published version
DDC subject of DNB:
510 Mathematics
Hosting institution:
Faculties, Faculty of Mathematics and Natural Sciences

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