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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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