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Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups

(2022) COLLECTANEA MATHEMATICA. 73(3). p.477-504
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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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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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