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 Lp-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.
Original language | English |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Colloquium Mathematicum |
Volume | 165 |
Issue number | 1 |
Early online date | 29 Oct 2020 |
DOIs | |
Publication status | Published - 31 Dec 2020 |
Keywords
- Analysis on Lie groups
- Fourier multipliers
- Graded nilpotent Lie groups
ASJC Scopus subject areas
- Mathematics(all)