Corpus ID: 119646538

Fourier multipliers on graded Lie groups

  title={Fourier multipliers on graded Lie groups},
  author={Veronique Fischer and M. Ruzhansky},
  journal={arXiv: Functional Analysis},
  • Veronique Fischer, M. Ruzhansky
  • Published 2014
  • Mathematics
  • arXiv: Functional Analysis
  • We study the $L^p$-boundedness of Fourier multipliers defined on graded nilpotent Lie groups via their group Fourier transform. We show that H\"ormander 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. 


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