The fractional Riesz transform and their commutator in Dunkl setting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910843355004928 |
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| author | Chen, Yanping Han, Xueting Wu, Liangchuan |
| author_facet | Chen, Yanping Han, Xueting Wu, Liangchuan |
| contents | In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness of their commutator with respect to the central BMO space associated with Euclidean metric and the BMO space associated with Dunkl metric, respectively. Based on this, we further characterize the compactness of the commutator in terms of the corresponding types of VMO spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_17884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fractional Riesz transform and their commutator in Dunkl setting Chen, Yanping Han, Xueting Wu, Liangchuan Classical Analysis and ODEs 42B35 (Primary) 43A85, 42B20 (Secondary) In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness of their commutator with respect to the central BMO space associated with Euclidean metric and the BMO space associated with Dunkl metric, respectively. Based on this, we further characterize the compactness of the commutator in terms of the corresponding types of VMO spaces. |
| title | The fractional Riesz transform and their commutator in Dunkl setting |
| topic | Classical Analysis and ODEs 42B35 (Primary) 43A85, 42B20 (Secondary) |
| url | https://arxiv.org/abs/2502.17884 |