Fourier Multipliers on Decomposition Spaces of Modulation and Triebel–Lizorkin Type

G. Cleanthous, Athanasios Georgiadis, Morten Nielsen

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Abstract

The family of anisotropic decomposition spaces of modulation and Triebel–Lizorkin type on Rn is a large family of smoothness spaces that include classical Besov, Triebel–Lizorkin, modulation and α-modulation spaces. The decomposition space approach allows for a unified treatment of such smoothness spaces in both the isotropic and an anisotropic setting. We derive a boundedness result for Fourier multipliers on anisotropic decomposition spaces of modulation and Triebel–Lizorkin type. As an application, we obtain equivalent quasi-norm characterizations for this class of decomposition spaces.
Original languageEnglish
JournalMediterranean Journal of Mathematics
Volume15
Issue number3
Number of pages14
ISSN1660-5446
DOIs
Publication statusPublished - 1 Jun 2018

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Keywords

  • Fourier multiplier
  • decompostion space
  • Triebel-Lizorkin space
  • Besov space

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