Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_ϕ$ spaces associated with Dunkl operator on the real line
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| Format: | Preprint |
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2025
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| _version_ | 1866915741015474176 |
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| author | Parashar, Sumit Adhikari, Saswata |
| author_facet | Parashar, Sumit Adhikari, Saswata |
| contents | The analysis of Morrey spaces, generalized Morrey spaces and $BMO_ϕ$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on $\mathbb{R}$ in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on $\mathbb{R}$ in Dunkl-type $BMO_ϕ$ spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_ϕ$ spaces associated with Dunkl operator on the real line Parashar, Sumit Adhikari, Saswata Classical Analysis and ODEs The analysis of Morrey spaces, generalized Morrey spaces and $BMO_ϕ$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on $\mathbb{R}$ in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on $\mathbb{R}$ in Dunkl-type $BMO_ϕ$ spaces. |
| title | Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_ϕ$ spaces associated with Dunkl operator on the real line |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2502.14390 |