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.
- Fourier multiplier
- decompostion space
- Triebel-Lizorkin space
- Besov space
Cleanthous, G., Georgiadis, A., & Nielsen, M. (2018). Fourier Multipliers on Decomposition Spaces of Modulation and Triebel–Lizorkin Type. Mediterranean Journal of Mathematics, 15(3). https://doi.org/10.1007/s00009-018-1171-3