Revista Matemática Iberoamericana


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Volume 35, Issue 5, 2019, pp. 1501–1534
DOI: 10.4171/rmi/1090

Published online: 2019-06-17

A multiplier theorem for sub-Laplacians with drift on Lie groups

Alessio Martini[1], Alessandro Ottazzi[2] and Maria Vallarino[3]

(1) University of Birmingham, UK
(2) University of New South Wales, Sydney, Australia
(3) Politecnico di Torino, Italy

We prove a general multiplier theorem for symmetric left-invariant sub-Laplacians with drift on non-compact Lie groups. This considerably improves and extends a result by Hebisch, Mauceri, and Meda. Applications include groups of polynomial growth and solvable extensions of stratified groups.

Keywords: Spectral multiplier, sub-Laplacian, Lie group, drift, Hardy space

Martini Alessio, Ottazzi Alessandro, Vallarino Maria: A multiplier theorem for sub-Laplacians with drift on Lie groups. Rev. Mat. Iberoam. 35 (2019), 1501-1534. doi: 10.4171/rmi/1090