Boundedness of commutator generated by fractional integral operator and Orlicz-BMO function
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| Format: | Preprint |
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2026
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| _version_ | 1866917442171699200 |
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| author | Zhuang, Zixing Fang, Chenglong Cao, Liwen |
| author_facet | Zhuang, Zixing Fang, Chenglong Cao, Liwen |
| contents | For $α\in(0, n)$ and a growth function $φ:[0,\infty)\rightarrow [0,\infty)$, it is proved that the commutator $[b,I_α]$ generated by fractional integral operator $I_α$ and Orlicz $\mathrm{BMO}$ function $b$ is bounded from Orlicz-Hardy space $H_{b}^φ(\mathbb{R}^{n})$ to Lebesgue space $L^{\frac{n}{n-α}}(\mathbb{R}^{n})$, where $H_{b}^φ(\mathbb{R}^{n})$ is a suitable Orlicz-Hardy space. Moreover, the authors also establish that the boundedness of commutator $[b,I_α]$ from Orlicz-Hardy space $H^φ(\mathbb{R}^{n})$ to weak Lebesgue space $L^{\frac{n}{n-α},\infty}(\mathbb{R}^{n})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23200 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundedness of commutator generated by fractional integral operator and Orlicz-BMO function Zhuang, Zixing Fang, Chenglong Cao, Liwen Functional Analysis For $α\in(0, n)$ and a growth function $φ:[0,\infty)\rightarrow [0,\infty)$, it is proved that the commutator $[b,I_α]$ generated by fractional integral operator $I_α$ and Orlicz $\mathrm{BMO}$ function $b$ is bounded from Orlicz-Hardy space $H_{b}^φ(\mathbb{R}^{n})$ to Lebesgue space $L^{\frac{n}{n-α}}(\mathbb{R}^{n})$, where $H_{b}^φ(\mathbb{R}^{n})$ is a suitable Orlicz-Hardy space. Moreover, the authors also establish that the boundedness of commutator $[b,I_α]$ from Orlicz-Hardy space $H^φ(\mathbb{R}^{n})$ to weak Lebesgue space $L^{\frac{n}{n-α},\infty}(\mathbb{R}^{n})$. |
| title | Boundedness of commutator generated by fractional integral operator and Orlicz-BMO function |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2604.23200 |