Abstract
The main purpose of this paper is three-fold. First, we prove that under the limited smoothness conditions, multi-parameter Fourier multiplier operators are bounded on multi-parameter Triebel-Lizorkin and Besov-Lipschitz spaces by the Littlewood-Paley decomposition and the strong maximal operator. Second, we offer a different and more direct method to deal with the boundedness instead of transforming Fourier multiplier operators into multi-parameter Calderón-Zygmund operators. Third, we also prove the boundedness of multi-parameter Fourier multiplier operators on weighted multi-parameter Triebel-Lizorkin and Besov-Lipschitz spaces when the Fourier multiplier is only assumed with limited smoothness.
| Original language | English |
|---|---|
| Pages (from-to) | 55-69 |
| Number of pages | 15 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 134 |
| DOIs | |
| Publication status | Published - 1 Mar 2016 |
| Externally published | Yes |
Keywords
- Littlewood-Paley decomposition
- Multi-parameter Besov-Lipschitz spaces
- Multi-parameter Fourier multiplier
- Multi-parameter Triebel-Lizorkin spaces
- Strong maximal functions
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Chen, L., Lu, G., & Luo, X. (2016). Boundedness of multi-parameter Fourier multiplier operators on Triebel-Lizorkin and Besov-Lipschitz spaces. Nonlinear Analysis, Theory, Methods and Applications, 134, 55-69. https://doi.org/10.1016/j.na.2015.12.016