Fourier multipliers on graded Lie groups
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 1-30
MSC: Primary 43A80; Secondary 43A22, 22E25.
DOI: 10.4064/cm7817-6-2020
Published online: 29 October 2020
Abstract
We study multipliers on graded nilpotent Lie groups defined via group Fourier transform. More precisely, we show that Hörmander-type conditions on the Fourier multipliers imply $L^p$-boundedness. We express these conditions using difference operators and positive Rockland operators. We also obtain a more refined condition using Sobolev spaces on the dual of the group which are defined and studied in this paper.
