
Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups
- Author
- Duvan Cardona Sanchez (UGent) and Michael Ruzhansky (UGent)
- Organization
- Project
- Abstract
- We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the Hormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Hormander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.
- Keywords
- Applied Mathematics, General Mathematics, Fourier multipliers, Spectral multipliers, Compact Lie groups, Hormander-Mihlin theorem, Marcinkiewicz condition, Triebel-Lizorkin spaces, PSEUDODIFFERENTIAL-OPERATORS, NIKOLSKII INEQUALITY, INVARIANT OPERATORS, BESOV CONTINUITY, THEOREMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01GYSSBSY52ABVG8JZYQ3YBYQY
- MLA
- Cardona Sanchez, Duvan, and Michael Ruzhansky. “Fourier Multipliers for Triebel–Lizorkin Spaces on Compact Lie Groups.” COLLECTANEA MATHEMATICA, vol. 73, no. 3, 2022, pp. 477–504, doi:10.1007/s13348-021-00330-9.
- APA
- Cardona Sanchez, D., & Ruzhansky, M. (2022). Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups. COLLECTANEA MATHEMATICA, 73(3), 477–504. https://doi.org/10.1007/s13348-021-00330-9
- Chicago author-date
- Cardona Sanchez, Duvan, and Michael Ruzhansky. 2022. “Fourier Multipliers for Triebel–Lizorkin Spaces on Compact Lie Groups.” COLLECTANEA MATHEMATICA 73 (3): 477–504. https://doi.org/10.1007/s13348-021-00330-9.
- Chicago author-date (all authors)
- Cardona Sanchez, Duvan, and Michael Ruzhansky. 2022. “Fourier Multipliers for Triebel–Lizorkin Spaces on Compact Lie Groups.” COLLECTANEA MATHEMATICA 73 (3): 477–504. doi:10.1007/s13348-021-00330-9.
- Vancouver
- 1.Cardona Sanchez D, Ruzhansky M. Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups. COLLECTANEA MATHEMATICA. 2022;73(3):477–504.
- IEEE
- [1]D. Cardona Sanchez and M. Ruzhansky, “Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups,” COLLECTANEA MATHEMATICA, vol. 73, no. 3, pp. 477–504, 2022.
@article{01GYSSBSY52ABVG8JZYQ3YBYQY, abstract = {{We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the Hormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Hormander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.}}, author = {{Cardona Sanchez, Duvan and Ruzhansky, Michael}}, issn = {{0010-0757}}, journal = {{COLLECTANEA MATHEMATICA}}, keywords = {{Applied Mathematics,General Mathematics,Fourier multipliers,Spectral multipliers,Compact Lie groups,Hormander-Mihlin theorem,Marcinkiewicz condition,Triebel-Lizorkin spaces,PSEUDODIFFERENTIAL-OPERATORS,NIKOLSKII INEQUALITY,INVARIANT OPERATORS,BESOV CONTINUITY,THEOREMS}}, language = {{eng}}, number = {{3}}, pages = {{477--504}}, title = {{Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups}}, url = {{http://doi.org/10.1007/s13348-021-00330-9}}, volume = {{73}}, year = {{2022}}, }
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