Spectral multipliers on two-step stratified Lie groups with degenerate group structure

2025/01/27 by Niedorf, Lars
#22E25 #22E30 #42B15 #43A85 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.16262

Abstract

Let L be a sub-Laplacian on a two-step stratified Lie group G of topological dimension d. We prove new L^p-spectral multiplier estimates under the sharp regularity condition s>d|1/p-1/2| in settings where the group structure of G is degenerate, extending previously known results for the non-degenerate case. Our results include variants of the free two-step nilpotent group on three generators and Heisenberg-Reiter groups. The proof combines restriction type estimates with a detailed analysis of the sub-Riemannian geometry of G. A key novelty of our approach is the use of a refined spectral decomposition into caps on the unit sphere in the center of the Lie group.

Related

• Spectral multipliers on Métivier groups
• Restriction type estimates on general two-step stratified Lie groups
• Restriction estimates for the free two step nilpotent group on three generators
• Strongly singular integrals on stratified groups
• Spectral multipliers for wave operators