A note on spectral multipliers on Engel and Cartan groups

Chatzakou, Marianna

doi:10.1090/proc/15830

A note on spectral multipliers on Engel and Cartan groups
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by Marianna Chatzakou PDF

Proc. Amer. Math. Soc. 150 (2022), 2259-2270 Request permission

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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