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G. Cleanthous, A. G. Georgiadis, and M. Nielsen. Fourier Multipliers on Decomposition Spaces of Modulation and Triebel--Lizorkin Type. Mediterranean Journal of Mathematics, 15(3):122, May 2018.
The family of anisotropic decomposition spaces of modulation and Triebel--Lizorkin type on \$\$\\backslashmathbb R\^n\$\$ R n is a large family of smoothness spaces that include classical Besov, Triebel--Lizorkin, modulation and \$\$\backslashalpha \$\$ $\alpha$ -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.
@article{Cleanthous2018,
Abstract = {The family of anisotropic decomposition spaces of modulation and Triebel--Lizorkin type on {\$}{\$}{\{}{\backslash}mathbb R{\}}^n{\$}{\$} R n is a large family of smoothness spaces that include classical Besov, Triebel--Lizorkin, modulation and {\$}{\$}{\backslash}alpha {\$}{\$} $\alpha$ -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.},
Author = {Cleanthous, G. and Georgiadis, A. G. and Nielsen, M.},
Bib2Html_Dl_Html = {https://doi.org/10.1007/s00009-018-1171-3},
Bib2Html_Pubtype = {Journal Article},
Date-Added = {2018-05-30 08:56:12 +0000},
Date-Modified = {2019-03-04 15:13:11 +0100},
Day = {19},
Issn = {1660-5454},
Journal = {Mediterranean Journal of Mathematics},
Month = {May},
Number = {3},
Pages = {122},
Title = {Fourier Multipliers on Decomposition Spaces of Modulation and Triebel--Lizorkin Type},
Volume = {15},
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1007/s00009-018-1171-3}}
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