Fourier multipliers on graded lie groups

Véronique Fischer, Michael Ruzhansky

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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 languageEnglish
Pages (from-to)1-30
Number of pages30
JournalColloquium Mathematicum
Volume165
Issue number1
Early online date29 Oct 2020
DOIs
Publication statusPublished - 2021

Keywords

  • Analysis on Lie groups
  • Fourier multipliers
  • Graded nilpotent Lie groups

ASJC Scopus subject areas

  • Mathematics(all)

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