A note on spectral multipliers on Engel and Cartan groups

2021/05/21 by Marianna Chatzakou, Chatzakou, M.
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Partial Differential Equations #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.10208

openalex publication_date 2021/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this short note is to give examples of L^p-L^q bounded spectral multipliers for operators involving left-invariant vector fields and their inverses, in the settings of Engel and Cartan groups. The interest in such examples lies in the fact that a group does not have to have flat co-adjoint orbits, and that the considered operator is not related to the usual sub-Laplacian. The discussed examples show how one can still obtain L^p-L^q estimates for similar operators in such settings. As immediate consequences, one gets the corresponding Sobolev-type inequalities and heat kernel estimates.

Citations

• Estimates for translation invariant operators in Lp spaces

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