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arXiv · 2105.10208

A note on spectral multipliers on Engel and Cartan groups

M. Chatzakou
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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.

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BibTeXRIS

M. Chatzakou. 2021-05-21. A note on spectral multipliers on Engel and Cartan groups. https://arxiv.org/abs/2105.10208

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