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

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Abstract

The family of anisotropic decomposition spaces of modulation and Triebel–Lizorkin type on \({\mathbb R}^n\) is a large family of smoothness spaces that include classical Besov, Triebel–Lizorkin, modulation and \(\alpha \)-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.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    G. Cleanthous

  2. Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    A. G. Georgiadis & M. Nielsen

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  1. G. Cleanthous
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  2. A. G. Georgiadis
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  3. M. Nielsen
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Correspondence to M. Nielsen.

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Cleanthous, G., Georgiadis, A.G. & Nielsen, M. Fourier Multipliers on Decomposition Spaces of Modulation and Triebel–Lizorkin Type. Mediterr. J. Math. 15, 122 (2018). https://doi.org/10.1007/s00009-018-1171-3

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  • DOI: https://doi.org/10.1007/s00009-018-1171-3

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